The boundedness of multilinear singular integrals of Calder′on-Zygmund type onproduct of variable exponent Lebesgue spaces over both bounded and unbounded domains areobtained. Further more, the boundedness for this t...The boundedness of multilinear singular integrals of Calder′on-Zygmund type onproduct of variable exponent Lebesgue spaces over both bounded and unbounded domains areobtained. Further more, the boundedness for this type multilinear operators on product ofvariable exponent Morrey spaces over domains is shown in the paper.展开更多
Wiener amalgam spaces are a class of function spaces where the function’s local and global behavior can be easily distinguished. These spaces are ex-tensively used in Harmonic analysis that originated in the work of ...Wiener amalgam spaces are a class of function spaces where the function’s local and global behavior can be easily distinguished. These spaces are ex-tensively used in Harmonic analysis that originated in the work of Wiener. In this paper: we first introduce a two-variable exponent amalgam space (L<sup>q</sup><sup>()</sup>,l<sup>p</sup><sup>()</sup>)(Ω). Secondly, we investigate some basic properties of these spaces, and finally, we study their dual.展开更多
Boundedness of multilinear singular integrals and their commutators from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces are obtained. The vector-valued case is also considered.
In this paper, by applying the technique of the sharp maximal function and the equivalent representation of the norm in the Lebesgue spaces with variable exponent, the boundedness of the parameterized Litflewood-Paley...In this paper, by applying the technique of the sharp maximal function and the equivalent representation of the norm in the Lebesgue spaces with variable exponent, the boundedness of the parameterized Litflewood-Paley operators, including the parameterized Lusin area integrals and the parameterized Littlewood-Paley gλ^＊- functions, is established on the Lebesgue spaces with variable exponent. Furthermore, the boundedness of their commutators generated respectively by BMO functions and Lipschitz functions are also obtained.展开更多
In this paper, we will discuss the behavior of a class of rough fractional integral operators on variable exponent Lebesgue spaces,and establish their boundedness from Lp1 （＇） （Rn） to Lp2（） （Rn）.
In this article, by extending classical Dellacherie＇s theorem on stochastic se- quences to variable exponent spaces, we prove that the famous Burkholder-Gundy-Davis in- equality holds for martingales in variable expo...In this article, by extending classical Dellacherie＇s theorem on stochastic se- quences to variable exponent spaces, we prove that the famous Burkholder-Gundy-Davis in- equality holds for martingales in variable exponent Hardy spaces. We also obtain the variable exponent analogues of several martingale inequalities in classical theory, including convexity lemma, Chevalier＇s inequality and the equivalence of two kinds of martingale spaces with predictable control. Moreover, under the regular condition on σ-algebra sequence we prove the equivalence between five kinds of variable exponent martingale Hardy spaces.展开更多
In [4], a new family W（L^p（x）, Lm^q） of Wiener amalgam spaces was defined and investigated some properties of these spaces, where local component is a variable exponent Lebesgue space L^p（x） （R） and the global...In [4], a new family W（L^p（x）, Lm^q） of Wiener amalgam spaces was defined and investigated some properties of these spaces, where local component is a variable exponent Lebesgue space L^p（x） （R） and the global component is a weighted Lebesgue space Lm^q （R）. This present paper is a sequel to our work [4]. In Section 2, we discuss necessary and sufficient conditions for the equality W （L^p（x）, Lm^q） = L^q （R）. Later we give some characterization of Wiener amalgam space W （L^p（x）, Lm^q）.In Section 3 we define the Wiener amalgam space W （FL^p（x）, Lm^q） and investigate some properties of this space, where FL^p（x） is the image of L^p（x） under the Fourier transform. In Section 4, we discuss boundedness of the Hardy- Littlewood maximal operator between some Wiener amalgam spaces.展开更多
We prove the boundedness of the maximal operator Mr in the spaces L^p（·）（Г,p） with variable exponent p（t） and power weight p on an arbitrary Carleson curve under the assumption that p（t） satisfies the lo...We prove the boundedness of the maximal operator Mr in the spaces L^p（·）（Г,p） with variable exponent p（t） and power weight p on an arbitrary Carleson curve under the assumption that p（t） satisfies the log-condition on Г. We prove also weighted Sobolev type L^p（·）（Г, p） → L^q（·）（Г, p）-theorem for potential operators on Carleson curves.展开更多
In this paper, we obtain the necessary and sufficient condition of the pre-compact sets in the variable exponent Lebesgue spaces, which is also called the Riesz-Kolmogorov theorem. The main novelty appearing in this a...In this paper, we obtain the necessary and sufficient condition of the pre-compact sets in the variable exponent Lebesgue spaces, which is also called the Riesz-Kolmogorov theorem. The main novelty appearing in this approach is the constructive approximation which does not rely on the boundedness of the Hardy-Littlewood maximal operator in the considered spaces such that we do not need the log-H¨older continuous conditions on the variable exponent. As applications, we establish the boundedness of Riemann-Liouville integral operators and prove the compactness of truncated Riemann-Liouville integral operators in the variable exponent Lebesgue spaces. Moreover, applying the Riesz-Kolmogorov theorem established in this paper, we obtain the existence and the uniqueness of solutions to a Cauchy type problem for fractional differential equations in variable exponent Lebesgue spaces.展开更多
We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.
This article is devoted to study the existence of renormalized solutions for the nonlinear p （x）-parabolic problem in the Weighted-Variable-Exponent Sobolev spaces, without the sign condition and the coercivity cond...This article is devoted to study the existence of renormalized solutions for the nonlinear p （x）-parabolic problem in the Weighted-Variable-Exponent Sobolev spaces, without the sign condition and the coercivity condition.展开更多
基金Supported by the National Natural Science Foundation of China (11071065, 10771110, 10471069)sponsored by the 151 Talent Fund of Zhejiang Province
文摘The boundedness of multilinear singular integrals of Calder′on-Zygmund type onproduct of variable exponent Lebesgue spaces over both bounded and unbounded domains areobtained. Further more, the boundedness for this type multilinear operators on product ofvariable exponent Morrey spaces over domains is shown in the paper.
文摘Wiener amalgam spaces are a class of function spaces where the function’s local and global behavior can be easily distinguished. These spaces are ex-tensively used in Harmonic analysis that originated in the work of Wiener. In this paper: we first introduce a two-variable exponent amalgam space (L<sup>q</sup><sup>()</sup>,l<sup>p</sup><sup>()</sup>)(Ω). Secondly, we investigate some basic properties of these spaces, and finally, we study their dual.
基金supported by the Scientific Research Fund of Hunan Provincial Education Department (09A058)
文摘Boundedness of multilinear singular integrals and their commutators from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces are obtained. The vector-valued case is also considered.
基金supported by National Natural Foundation of China (Grant Nos. 11161042 and 11071250)
文摘In this paper, by applying the technique of the sharp maximal function and the equivalent representation of the norm in the Lebesgue spaces with variable exponent, the boundedness of the parameterized Litflewood-Paley operators, including the parameterized Lusin area integrals and the parameterized Littlewood-Paley gλ^＊- functions, is established on the Lebesgue spaces with variable exponent. Furthermore, the boundedness of their commutators generated respectively by BMO functions and Lipschitz functions are also obtained.
基金Supported by the NSF of Zhejiang Province (Y6090681)the Education Dept.of Zhejiang Province(Y201120509)
文摘In this paper, we will discuss the behavior of a class of rough fractional integral operators on variable exponent Lebesgue spaces,and establish their boundedness from Lp1 （＇） （Rn） to Lp2（） （Rn）.
基金supported by NSFC(11471251)supported by NSFC(11271293)
文摘In this article, by extending classical Dellacherie＇s theorem on stochastic se- quences to variable exponent spaces, we prove that the famous Burkholder-Gundy-Davis in- equality holds for martingales in variable exponent Hardy spaces. We also obtain the variable exponent analogues of several martingale inequalities in classical theory, including convexity lemma, Chevalier＇s inequality and the equivalence of two kinds of martingale spaces with predictable control. Moreover, under the regular condition on σ-algebra sequence we prove the equivalence between five kinds of variable exponent martingale Hardy spaces.
文摘In [4], a new family W（L^p（x）, Lm^q） of Wiener amalgam spaces was defined and investigated some properties of these spaces, where local component is a variable exponent Lebesgue space L^p（x） （R） and the global component is a weighted Lebesgue space Lm^q （R）. This present paper is a sequel to our work [4]. In Section 2, we discuss necessary and sufficient conditions for the equality W （L^p（x）, Lm^q） = L^q （R）. Later we give some characterization of Wiener amalgam space W （L^p（x）, Lm^q）.In Section 3 we define the Wiener amalgam space W （FL^p（x）, Lm^q） and investigate some properties of this space, where FL^p（x） is the image of L^p（x） under the Fourier transform. In Section 4, we discuss boundedness of the Hardy- Littlewood maximal operator between some Wiener amalgam spaces.
文摘We prove the boundedness of the maximal operator Mr in the spaces L^p（·）（Г,p） with variable exponent p（t） and power weight p on an arbitrary Carleson curve under the assumption that p（t） satisfies the log-condition on Г. We prove also weighted Sobolev type L^p（·）（Г, p） → L^q（·）（Г, p）-theorem for potential operators on Carleson curves.
基金supported by the Startup Foundation for Introducing Talent of Nanjing University of Information Science and Technology(Grant No.2017r098)Zunwei Fu was supported by National Natural Science Foundation of China(Grant Nos.11671185 and 11771195)+1 种基金National Science Foundation of Shandong Province(Grant No.ZR2017MA041)Jingshi Xu was supported by National Natural Science Foundation of China(Grant No.11761026)
文摘In this paper, we obtain the necessary and sufficient condition of the pre-compact sets in the variable exponent Lebesgue spaces, which is also called the Riesz-Kolmogorov theorem. The main novelty appearing in this approach is the constructive approximation which does not rely on the boundedness of the Hardy-Littlewood maximal operator in the considered spaces such that we do not need the log-H¨older continuous conditions on the variable exponent. As applications, we establish the boundedness of Riemann-Liouville integral operators and prove the compactness of truncated Riemann-Liouville integral operators in the variable exponent Lebesgue spaces. Moreover, applying the Riesz-Kolmogorov theorem established in this paper, we obtain the existence and the uniqueness of solutions to a Cauchy type problem for fractional differential equations in variable exponent Lebesgue spaces.
文摘We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.
文摘This article is devoted to study the existence of renormalized solutions for the nonlinear p （x）-parabolic problem in the Weighted-Variable-Exponent Sobolev spaces, without the sign condition and the coercivity condition.
