The boundness and compactness of products of multiplication,composition and differentiation on weighted Bergman spaces in the unit ball are studied.We define the differentiation operator on the space of holomorphic fu...The boundness and compactness of products of multiplication,composition and differentiation on weighted Bergman spaces in the unit ball are studied.We define the differentiation operator on the space of holomorphic functions in the unit ball by radial derivative.Then we extend the Sharma's results.展开更多
Integrating autonomous vehicles (AVs) and autonomous parking spaces (APS) marks a transformative development in urban mobility and sustainability. This paper reflects on these technologies’ historical evolution, curr...Integrating autonomous vehicles (AVs) and autonomous parking spaces (APS) marks a transformative development in urban mobility and sustainability. This paper reflects on these technologies’ historical evolution, current interdependence, and future potential through the lens of environmental, social, and economic sustainability. Historically, parking systems evolved from manual designs to automated processes yet remained focused on convenience rather than sustainability. Presently, advancements in smart infrastructure and vehicle-to-infrastructure (V2I) communication have enabled AVs and APS to operate as a cohesive system, optimizing space, energy, and transportation efficiency. Looking ahead, the seamless integration of AVs and APS into broader smart city ecosystems promises to redefine urban landscapes by repurposing traditional parking infrastructure into multifunctional spaces and supporting renewable energy initiatives. These technologies align with global sustainability goals by mitigating emissions, reducing urban sprawl, and fostering adaptive land uses. This reflection highlights the need for collaborative efforts among stakeholders to address regulatory and technological challenges, ensuring the equitable and efficient deployment of AVs and APS for smarter, greener cities.展开更多
In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in C^(n).We observe that H_(f ) is bounded on H~p(Ω)(1 <p <∞) if f belongs to BMO a...In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in C^(n).We observe that H_(f ) is bounded on H~p(Ω)(1 <p <∞) if f belongs to BMO and we obtain some characterizations for Hf on H^(2)(Ω) of other pseudoconvex domains.In these arguments,Amar's L^(p)-estimations and Berndtsson's L^(2)-estimations for solutions of the ■_(b)-equation play a crucial role.In addition,we solve Gleason's problem for Hardy spaces H^(p)(Ω)(1 ≤p≤∞) of bounded strongly pseudoconvex domains.展开更多
In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type spaces.In order t...In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type spaces.In order to prove the main results,we first give some bidirectional estimates for several typical integrals.展开更多
For analytic functions u,ψin the unit disk D in the complex plane and an analytic self-mapφof D,we describe in this paper the boundedness and compactness of product type operators T_(u,ψ,φ)f(z)=u(z)f(φ(z))+ψ(z)f...For analytic functions u,ψin the unit disk D in the complex plane and an analytic self-mapφof D,we describe in this paper the boundedness and compactness of product type operators T_(u,ψ,φ)f(z)=u(z)f(φ(z))+ψ(z)f'(φ(z)),z∈D,acting between weighted Bergman spaces induced by a doubling weight and a Bloch type space with a radial weight.展开更多
Urbanization has profound impacts on ecological environments. Green spaces are a vital component of urban ecosystems and play a crucial role in maintaining ecological balance and enhancing sustainability. This study a...Urbanization has profound impacts on ecological environments. Green spaces are a vital component of urban ecosystems and play a crucial role in maintaining ecological balance and enhancing sustainability. This study aimed to investigate the community composition characteristics of butterflies in urban green spaces within the context of rapid urbanization. Simultaneously, it explored the status and differences in butterfly taxonomic diversity, functional diversity, and functional traits among different types of urban green spaces, regions, and urban gradients to provide relevant insights for further improving urban green space quality and promoting biodiversity conservation. We conducted a year-long survey of 80 green spaces across different urban regions and ring roads within Hefei City, Anhui Province, with monthly sampling intervals over 187 transects. A total of 4822 butterflies, belonging to 5 families, 17 subfamilies, 40 genera, and 55 species were identified. The species richness, Shannon, Simpson, functional richness, and Rao's quadratic entropy indices of butterflies in urban park green spaces were all significantly higher than those in residential and street green spaces(P < 0.05). Differences in butterfly diversity and functional traits among different urban regions and ring roads were relatively minor, and small-sized, multivoltine, and long flying duration butterflies dominated urban green spaces. Overall, these spaces offer more favorable habitats for butterflies. However, some residential green spaces and street green spaces demonstrate potential for butterfly conservation.展开更多
Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying som...Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild assumptions.Let HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.展开更多
The Q_(K)(p)-Teichmüller space is introduced and studied in this paper.Various characterizations of the Q_(K)(p)-Teichmüller space and the Q_(K,0)(p)-Teichmüller space are given.Their Schwarzian derivat...The Q_(K)(p)-Teichmüller space is introduced and studied in this paper.Various characterizations of the Q_(K)(p)-Teichmüller space and the Q_(K,0)(p)-Teichmüller space are given.Their Schwarzian derivative model and pre-logarithmic derivative model are also discussed.展开更多
Letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entriesμn,k=μn+k,whereμn=■[0,1)tndμ(t),induces,formally,the operator■where■is an analytic function in.We characterize the measuresμ...Letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entriesμn,k=μn+k,whereμn=■[0,1)tndμ(t),induces,formally,the operator■where■is an analytic function in.We characterize the measuresμfor which■is bounded(resp.,compact)operator from the logarithmic Bloch space■into the Bergman space■,where 0≤α<∞,0<p<∞.We also characterize the measuresμfor which■is bounded(resp.,compact)operator from the logarithmic Bloch space■into the classical Bloch space■.展开更多
In this paper,we study multiplication operators on weighted Dirichlet spaces D_(β)(β∈R).Let n be a positive integer and β∈R,we show that the multiplication operator M_(z)^(n) on D_(β) is similar to the operator ...In this paper,we study multiplication operators on weighted Dirichlet spaces D_(β)(β∈R).Let n be a positive integer and β∈R,we show that the multiplication operator M_(z)^(n) on D_(β) is similar to the operator ⊕_(1)^(n)M_(z)on the space⊕_(1)^(n)D_(β).Moreover,we prove that M_(z)^(n)(≥2)on Dβis unitarily equivalent to ⊕_(1)^(n)M_(z) on⊕_(1)^(n)D_(β) if and only if β=0.In addition,we completely characterize the unitary equivalence of the restrictions of M_(z)^(n) to different invariant subspaces z^(k)D_(β)(k≥1),and the unitary equivalence of the restrictions of M_(z)^(n) to different invariant subspaces S_(j)(0≤j<n).Abkar,Cao and Zhu[Complex Anal Oper Theory,2020,14:Art 58]pointed out that it is an important,natural,and difficult question in operator theory to identify the commutant of a bounded linear operator.They characterized the commutant A′( M_(z)^(n))of M_(z)^(n)on a family of analytic function spaces A_(α)^(2)(α∈R)on D(in fact,the family of spaces A_(α)^(2)(α∈R)is the same with the family of spaces D_(β)(β∈R))in terms of the multiplier algebra of the underlying function spaces.In this paper,we give a new characterization of the commutant A′( M_(z)^(n))of M_(z)^(n)on D_(β),and characterize the self-adjoint operators and unitary operators in A'(M_(z)^(n)).We find that the class of self-adjoint operators(unitary operators)in A'(M_(z)^(n))when β≠0 is different from the class of self-adjoint operators(unitary operators)in A′( M_(z)^(n))when β=0.展开更多
We consider dual Toeplitz operators on the orthogonal complements of the FockSobolev spaces of all nonnegative real orders.First,for symbols in a certain class containing all bounded functions,we study the problem of ...We consider dual Toeplitz operators on the orthogonal complements of the FockSobolev spaces of all nonnegative real orders.First,for symbols in a certain class containing all bounded functions,we study the problem of when an operator which is finite sums of the dual Toeplitz products is compact or zero.Next,for bounded symbols,we construct a symbol map and exhibit a short exact sequence associated with the C^(*)-algebra generated by all dual Toeplitz operators with bounded symbols.展开更多
In this paper,we study a kind of curvature flow in warped product spaces.We obtain convergence results under barrier conditions and restrictions on prescribed function.We also obtain the asymptotic behavior of a kind ...In this paper,we study a kind of curvature flow in warped product spaces.We obtain convergence results under barrier conditions and restrictions on prescribed function.We also obtain the asymptotic behavior of a kind of inverse curvature flow in Schwarzschild manifold.展开更多
In this paper,we introduce the weighted multilinear p-adic Hardy operator and weighted multilinear p-adic Ces`aro operator,we also obtain the boundedness of these two operators on the product of p-adic Herz spaces and...In this paper,we introduce the weighted multilinear p-adic Hardy operator and weighted multilinear p-adic Ces`aro operator,we also obtain the boundedness of these two operators on the product of p-adic Herz spaces and p-adic Morrey-Herz spaces,the corresponding operator norms are also established in each case.Moreover,the boundedness of commutators of these two operators with symbols in central bounded mean oscillation spaces and Lipschitz spaces on p-adic Morrey-Herz spaces are also given.展开更多
Urbanization often changes bird species richness and affects the functional diversity.Therefore,understanding these changes helps city planners improve green space design and land use planning.Our study used multiple ...Urbanization often changes bird species richness and affects the functional diversity.Therefore,understanding these changes helps city planners improve green space design and land use planning.Our study used multiple datasets to explore the effects of land-scape patterns and natural environments on the functional diversity of birds in urban parks and campuses in the eastern and northwest-ern regions of China.Firstly,we used the data to calculate birds of the functional richness(FRic),functional evenness(FEve),and functional divergence(FDiv)of 68 urban spaces in the eastern and northwestern regions of China.Further,we established generalized linear models of natural factors,human factors,and functional diversity.Results showed more bird species with unique traits were in the north-western region.This may be because the earlier urbanization in the eastern region filtered out urban-sensitive species,leaving behind urban adapters.Moreover,we found that the fractal dimension index was the most significant positive factor of FRic in the eastern region but the most significant negative factor of FDiv.Elevation was the most significant negative influence factor of FEve in the eastern region,but it was the most potent positive influence factor of FRic in the northwestern region.Population density had a significant positive effect on FDiv in the northwestern region.However,green space areas significantly negatively impacted FEve in the northwestern region.In addition,birds in parks in both regions had more functional traits than those on campuses,possibly because of the larger green space in parks,which may contain more fragments of native vegetation and reduce human interference.Our study suggests that preserving more original vegetation and reducing human disturbance in cities can increase the functional diversity of urban birds and im-prove urban ecosystem functions.展开更多
In this paper,by characterizing Carleson measures,we investigate a class of bounded Toeplitz operator between weighted Bergman spaces with Békolléweights over the half-plane for all index choices.
In this paper,we study the trigonometric approximation problems of functions which belong to the Lipαclass,the Lip(ξ(t))class,and the W(L_(M)^(*);ξ(t))class in Orlicz spaces by using the tools Hölder inequalit...In this paper,we study the trigonometric approximation problems of functions which belong to the Lipαclass,the Lip(ξ(t))class,and the W(L_(M)^(*);ξ(t))class in Orlicz spaces by using the tools Hölder inequality in Orlicz spaces,the second mean value theorem for integrals,and(E,q)(C,α,β)means etc.At the same time,we give the corresponding degree of approximation.展开更多
Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting...Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.展开更多
基金Supported by Natural Science Foundation of Guangdong Province in China(2018KTSCX161)。
文摘The boundness and compactness of products of multiplication,composition and differentiation on weighted Bergman spaces in the unit ball are studied.We define the differentiation operator on the space of holomorphic functions in the unit ball by radial derivative.Then we extend the Sharma's results.
文摘Integrating autonomous vehicles (AVs) and autonomous parking spaces (APS) marks a transformative development in urban mobility and sustainability. This paper reflects on these technologies’ historical evolution, current interdependence, and future potential through the lens of environmental, social, and economic sustainability. Historically, parking systems evolved from manual designs to automated processes yet remained focused on convenience rather than sustainability. Presently, advancements in smart infrastructure and vehicle-to-infrastructure (V2I) communication have enabled AVs and APS to operate as a cohesive system, optimizing space, energy, and transportation efficiency. Looking ahead, the seamless integration of AVs and APS into broader smart city ecosystems promises to redefine urban landscapes by repurposing traditional parking infrastructure into multifunctional spaces and supporting renewable energy initiatives. These technologies align with global sustainability goals by mitigating emissions, reducing urban sprawl, and fostering adaptive land uses. This reflection highlights the need for collaborative efforts among stakeholders to address regulatory and technological challenges, ensuring the equitable and efficient deployment of AVs and APS for smarter, greener cities.
基金supported by the National Natural Science Foundation of China(12271101)。
文摘In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in C^(n).We observe that H_(f ) is bounded on H~p(Ω)(1 <p <∞) if f belongs to BMO and we obtain some characterizations for Hf on H^(2)(Ω) of other pseudoconvex domains.In these arguments,Amar's L^(p)-estimations and Berndtsson's L^(2)-estimations for solutions of the ■_(b)-equation play a crucial role.In addition,we solve Gleason's problem for Hardy spaces H^(p)(Ω)(1 ≤p≤∞) of bounded strongly pseudoconvex domains.
基金supported by the Natural Science Foundation of Hunan Province of China(2022JJ30369)the Education Department Important Foundation of Hunan Province in China(23A0095)。
文摘In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type spaces.In order to prove the main results,we first give some bidirectional estimates for several typical integrals.
文摘For analytic functions u,ψin the unit disk D in the complex plane and an analytic self-mapφof D,we describe in this paper the boundedness and compactness of product type operators T_(u,ψ,φ)f(z)=u(z)f(φ(z))+ψ(z)f'(φ(z)),z∈D,acting between weighted Bergman spaces induced by a doubling weight and a Bloch type space with a radial weight.
基金funded by the National Non Profit Research Institutions of the Chinese Academy of Forestry(CAFYBB2020ZB008)National Natural Science Foundation of China(32371936)the Research Projects in Anhui Universities in 2022(natural sciences)(2022AH051874).
文摘Urbanization has profound impacts on ecological environments. Green spaces are a vital component of urban ecosystems and play a crucial role in maintaining ecological balance and enhancing sustainability. This study aimed to investigate the community composition characteristics of butterflies in urban green spaces within the context of rapid urbanization. Simultaneously, it explored the status and differences in butterfly taxonomic diversity, functional diversity, and functional traits among different types of urban green spaces, regions, and urban gradients to provide relevant insights for further improving urban green space quality and promoting biodiversity conservation. We conducted a year-long survey of 80 green spaces across different urban regions and ring roads within Hefei City, Anhui Province, with monthly sampling intervals over 187 transects. A total of 4822 butterflies, belonging to 5 families, 17 subfamilies, 40 genera, and 55 species were identified. The species richness, Shannon, Simpson, functional richness, and Rao's quadratic entropy indices of butterflies in urban park green spaces were all significantly higher than those in residential and street green spaces(P < 0.05). Differences in butterfly diversity and functional traits among different urban regions and ring roads were relatively minor, and small-sized, multivoltine, and long flying duration butterflies dominated urban green spaces. Overall, these spaces offer more favorable habitats for butterflies. However, some residential green spaces and street green spaces demonstrate potential for butterfly conservation.
基金supported by the National Key Research and Development Program of China(2020YFA0712900)the National Natural Science Foundation of China(12371093,12071197,12122102 and 12071431)+2 种基金the Key Project of Gansu Provincial National Science Foundation(23JRRA1022)the Fundamental Research Funds for the Central Universities(2233300008 and lzujbky-2021-ey18)the Innovative Groups of Basic Research in Gansu Province(22JR5RA391).
文摘Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild assumptions.Let HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.
基金supported by the National Natural Science Foundation of China(12271017)supported by the Natural Science Foundation of Shandong Province(ZR2022MA018)by the National Natural Science Foundation of China(12171221)。
文摘The Q_(K)(p)-Teichmüller space is introduced and studied in this paper.Various characterizations of the Q_(K)(p)-Teichmüller space and the Q_(K,0)(p)-Teichmüller space are given.Their Schwarzian derivative model and pre-logarithmic derivative model are also discussed.
基金supported by Zhejiang Provincial Natural Science Foundation of China(LY23A010003).
文摘Letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entriesμn,k=μn+k,whereμn=■[0,1)tndμ(t),induces,formally,the operator■where■is an analytic function in.We characterize the measuresμfor which■is bounded(resp.,compact)operator from the logarithmic Bloch space■into the Bergman space■,where 0≤α<∞,0<p<∞.We also characterize the measuresμfor which■is bounded(resp.,compact)operator from the logarithmic Bloch space■into the classical Bloch space■.
基金supported by the National Natural Science Foundation of China(12101179,12171138,12171373)the Natural Science Foundation of Hebei Province of China(A2022207001)。
文摘In this paper,we study multiplication operators on weighted Dirichlet spaces D_(β)(β∈R).Let n be a positive integer and β∈R,we show that the multiplication operator M_(z)^(n) on D_(β) is similar to the operator ⊕_(1)^(n)M_(z)on the space⊕_(1)^(n)D_(β).Moreover,we prove that M_(z)^(n)(≥2)on Dβis unitarily equivalent to ⊕_(1)^(n)M_(z) on⊕_(1)^(n)D_(β) if and only if β=0.In addition,we completely characterize the unitary equivalence of the restrictions of M_(z)^(n) to different invariant subspaces z^(k)D_(β)(k≥1),and the unitary equivalence of the restrictions of M_(z)^(n) to different invariant subspaces S_(j)(0≤j<n).Abkar,Cao and Zhu[Complex Anal Oper Theory,2020,14:Art 58]pointed out that it is an important,natural,and difficult question in operator theory to identify the commutant of a bounded linear operator.They characterized the commutant A′( M_(z)^(n))of M_(z)^(n)on a family of analytic function spaces A_(α)^(2)(α∈R)on D(in fact,the family of spaces A_(α)^(2)(α∈R)is the same with the family of spaces D_(β)(β∈R))in terms of the multiplier algebra of the underlying function spaces.In this paper,we give a new characterization of the commutant A′( M_(z)^(n))of M_(z)^(n)on D_(β),and characterize the self-adjoint operators and unitary operators in A'(M_(z)^(n)).We find that the class of self-adjoint operators(unitary operators)in A'(M_(z)^(n))when β≠0 is different from the class of self-adjoint operators(unitary operators)in A′( M_(z)^(n))when β=0.
基金supported by the NSFC(12271134,11771401)supported by the Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(NRF-2019R1I1A3A01041943)。
文摘We consider dual Toeplitz operators on the orthogonal complements of the FockSobolev spaces of all nonnegative real orders.First,for symbols in a certain class containing all bounded functions,we study the problem of when an operator which is finite sums of the dual Toeplitz products is compact or zero.Next,for bounded symbols,we construct a symbol map and exhibit a short exact sequence associated with the C^(*)-algebra generated by all dual Toeplitz operators with bounded symbols.
基金Supported by the National Natural Science Foundation of China(12031017 and 11971424).
文摘In this paper,we study a kind of curvature flow in warped product spaces.We obtain convergence results under barrier conditions and restrictions on prescribed function.We also obtain the asymptotic behavior of a kind of inverse curvature flow in Schwarzschild manifold.
文摘In this paper,we introduce the weighted multilinear p-adic Hardy operator and weighted multilinear p-adic Ces`aro operator,we also obtain the boundedness of these two operators on the product of p-adic Herz spaces and p-adic Morrey-Herz spaces,the corresponding operator norms are also established in each case.Moreover,the boundedness of commutators of these two operators with symbols in central bounded mean oscillation spaces and Lipschitz spaces on p-adic Morrey-Herz spaces are also given.
基金Under the auspices of the Innovation Program of Chinese Academy of Agricultural Sciences(No.CAAS-STNY-2024)。
文摘Urbanization often changes bird species richness and affects the functional diversity.Therefore,understanding these changes helps city planners improve green space design and land use planning.Our study used multiple datasets to explore the effects of land-scape patterns and natural environments on the functional diversity of birds in urban parks and campuses in the eastern and northwest-ern regions of China.Firstly,we used the data to calculate birds of the functional richness(FRic),functional evenness(FEve),and functional divergence(FDiv)of 68 urban spaces in the eastern and northwestern regions of China.Further,we established generalized linear models of natural factors,human factors,and functional diversity.Results showed more bird species with unique traits were in the north-western region.This may be because the earlier urbanization in the eastern region filtered out urban-sensitive species,leaving behind urban adapters.Moreover,we found that the fractal dimension index was the most significant positive factor of FRic in the eastern region but the most significant negative factor of FDiv.Elevation was the most significant negative influence factor of FEve in the eastern region,but it was the most potent positive influence factor of FRic in the northwestern region.Population density had a significant positive effect on FDiv in the northwestern region.However,green space areas significantly negatively impacted FEve in the northwestern region.In addition,birds in parks in both regions had more functional traits than those on campuses,possibly because of the larger green space in parks,which may contain more fragments of native vegetation and reduce human interference.Our study suggests that preserving more original vegetation and reducing human disturbance in cities can increase the functional diversity of urban birds and im-prove urban ecosystem functions.
基金supported by the Natural Science Foundation of China(12271134)the Shanxi Scholarship Council of China(2020–089)the Fund Program for the Scientific Activities of Selected Returned Overseas Professionals in Shanxi Province(20200019).
文摘In this paper,by characterizing Carleson measures,we investigate a class of bounded Toeplitz operator between weighted Bergman spaces with Békolléweights over the half-plane for all index choices.
基金Supported by the National Natural Science Foundation of China(Grant No.11761055)The Fundamental Research Funds for the Inner Mongolia Normal University(Grant No.2023JBZD007)+1 种基金The First-Class Disciplines Project,Inner Mongolia Autonomous Region(Grant No.YLXKZX-NSD-001)Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region(Grant No.NMGIRT2414).
文摘In this paper,we study the trigonometric approximation problems of functions which belong to the Lipαclass,the Lip(ξ(t))class,and the W(L_(M)^(*);ξ(t))class in Orlicz spaces by using the tools Hölder inequality in Orlicz spaces,the second mean value theorem for integrals,and(E,q)(C,α,β)means etc.At the same time,we give the corresponding degree of approximation.
文摘Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.
