In this paper, we will obtain the weak type estimates of intrinsic square func- tions including the Lusin area integral, Littlewood-Paley g-function and g^-function on the weighted Morrey spaces L^1,k （w） for 0〈k〈...In this paper, we will obtain the weak type estimates of intrinsic square func- tions including the Lusin area integral, Littlewood-Paley g-function and g^-function on the weighted Morrey spaces L^1,k （w） for 0〈k〈 1 and w ∈ A1.展开更多
In this note, we consider the multipliers on weighted function spaces over totally disconnected locally compact abelian groups (Vilenkin groups). Firstly we show an (H1 ,L ) multiplier result. We also give an (Hap ,Ha...In this note, we consider the multipliers on weighted function spaces over totally disconnected locally compact abelian groups (Vilenkin groups). Firstly we show an (H1 ,L ) multiplier result. We also give an (Hap ,Hap) multiplier result under a similiar condition of Lu Yang type. In section 2, we obtain a result about the boundedness of multipliers on weighted Besov spaces.展开更多
We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applic...We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applications, we also give estimates of the es- sential norms of weighted composition operators between weighted Banach space of analytic functions and Bloch-type spaces.展开更多
In this article, we study the boundedness of weighted composition operators between different vector-valued Dirichlet spaces. Some sufficient and necessary conditions for such operators to be bounded are obtained exac...In this article, we study the boundedness of weighted composition operators between different vector-valued Dirichlet spaces. Some sufficient and necessary conditions for such operators to be bounded are obtained exactly, which are different completely from the scalar-valued case. As applications, we show that these vector-valued Dirichlet spaces are different counterparts of the classical scalar-valued Dirichlet space and characterize the boundedness of multiplication operators between these different spaces.展开更多
Suppose T^k,l and T^k,2 are singular integrals with variable kernels and mixed homogeneity or ±I （the identity operator）. Denote the Toeplitz type operator by T^b=k=1∑^QT^k,1M^bT^k,2 where M^bf= bf. In this pa...Suppose T^k,l and T^k,2 are singular integrals with variable kernels and mixed homogeneity or ±I （the identity operator）. Denote the Toeplitz type operator by T^b=k=1∑^QT^k,1M^bT^k,2 where M^bf= bf. In this paper, the boundedness of Tb on weighted Morrey space are obtained when b belongs to the weighted Lipschitz function space and weighted BMO function space, respectively.展开更多
In this paper we consider the Nemytskii operator, i.e., the composition operator defined by (Nf)(t)=H(t,f(t)), where H is a given set-valued function. It is shown that if the operator N maps the space of functions bou...In this paper we consider the Nemytskii operator, i.e., the composition operator defined by (Nf)(t)=H(t,f(t)), where H is a given set-valued function. It is shown that if the operator N maps the space of functions bounded φ1-variation in the sense of Riesz with respect to the weight function αinto the space of set-valued functions of bounded φ2-variation in the sense of Riesz with respect to the weight, if it is globally Lipschitzian, then it has to be of the form (Nf)(t)=A(t)f(t)+B(t), where A(t) is a linear continuous set-valued function and B is a set-valued function of bounded φ2-variation in the sense of Riesz with respect to the weight.展开更多
In this paper, several new results on the boundedness of parammetric Marcinkiewicz integrals on the weighted Hardy spaces and the weak weighted Hardy spaces are established.
In this paper, we will use a method of sharp maximal function approach to show the boundedness of commutator [b,TR^δ] by Bochner-Riesz operators and the function b on weighted Morrey spaces L^p,k （ω） under appro...In this paper, we will use a method of sharp maximal function approach to show the boundedness of commutator [b,TR^δ] by Bochner-Riesz operators and the function b on weighted Morrey spaces L^p,k （ω） under appropriate conditions on the weight w, where b belongs to Lipschitz space or weighted Lipschitz space.展开更多
We characterize boundedness and compactness of products of differentiation op- erators and weighted composition operators between weighted Banach spaces of analytic functions and weighted Zygmund spaces or weighted Bl...We characterize boundedness and compactness of products of differentiation op- erators and weighted composition operators between weighted Banach spaces of analytic functions and weighted Zygmund spaces or weighted Bloch spaces with general weights.展开更多
We characterize the boundedness and compactness of weighted composition operators on weighted Dirichlet spaces in terms of Nevanlinna counting functions and Caxleson measure.
In this article, we obtain the LP-boundedness of commutators of Lipschitz functions and singular integrals with non-smooth kernels on Euclidean spaces.
[b,T] denotes the commutator of generalized Calderon-Zygmund operators T with Lipschitz function b, where b∈Lip;（R;）,（0 <β≤1） and T is aθ（t）-type Calderón-Zygmund operator. The commutator [b,T] gener...[b,T] denotes the commutator of generalized Calderon-Zygmund operators T with Lipschitz function b, where b∈Lip;（R;）,（0 <β≤1） and T is aθ（t）-type Calderón-Zygmund operator. The commutator [b,T] generated by b and T is defined by[b,T]f（x）=b（x）Tf（x）-T（bf）(x)=∫k（x,y）(b（x）-b（y）)f（y）dy.In this paper, the authors discuss the boundedness of the commutator [b, T] on weighted Hardy spaces and weighted Herz type Hardy spaces and prove that [b,T] is bounded from H;（ω;） to L;（ω;）, and from HK;(ω;,ω;) to K;(ω;,ω;). The results extend and generalize the well-known ones in [7].展开更多
In account of the famous Cebysev inequality, a rich theory has appeared in the literature. We establish some new weighted Cebysev type integral inequalities. Our proofs are of independent interest and provide new esti...In account of the famous Cebysev inequality, a rich theory has appeared in the literature. We establish some new weighted Cebysev type integral inequalities. Our proofs are of independent interest and provide new estimates on these types of inequalities.展开更多
目的探讨近期皮质下小梗死(RSSI)患者颅内深髓静脉(DMV)可见性与不同区域血管周围间隙扩大(EPVS)及认知功能的相关性。方法回顾性连续纳入南京医科大学附属常州市第二人民医院神经内科自2022年10月至2023年10月收治的RSSI患者,所有患者...目的探讨近期皮质下小梗死(RSSI)患者颅内深髓静脉(DMV)可见性与不同区域血管周围间隙扩大(EPVS)及认知功能的相关性。方法回顾性连续纳入南京医科大学附属常州市第二人民医院神经内科自2022年10月至2023年10月收治的RSSI患者,所有患者入院后3 d内完成MR的常规及磁敏感加权成像(SWI)序列扫描。所有RSSI患者发病7 d内进行蒙特利尔认知评估(MoCA)量表评分。对所有患者基底节区(BG)和半卵圆中心区的EPVS进行分级评估和体积测量,使用DMV视觉评分对患者SWI幅度图或最小强度投影图上的DMV可见性进行评估,并将患者分为可见性较高的DMV低-中分组(评分0~12分,104例)及可见性较低的DMV高分组(评分13~18分,47例),采用单因素分析比较两组患者的临床和影像学资料,采用多因素Logistic回归和Spearman相关分析方法分析DMV可见性与BG-EPVS分级及体积的关系以及其与患者认知功能的关系。结果共纳入RSSI患者151例,平均年龄(69±10)岁,其中男92例(60.9%),女59例(39.1%)。DMV高分组RSSI患者的年龄[(76±5)岁比(65±10)岁,t=-10.875]、高血压病患者比例[78.7%(37/47)比54.8%(57/104),χ^(2)=7.879]、BG-EPVS分级、BG-EPVS体积[5.67(5.30,5.81)ln mm 3比4.61(3.66,5.30)ln mm 3,Z=-6.772]、脑白质高信号体积[7.67(6.23,8.43)ln mm 3比4.31(3.53,5.89)ln mm 3,Z=-6.501]均明显高于DMV低-中分组,差异均有统计学意义(均P<0.05)。DMV高分组RSSI患者的总胆固醇[3.74(3.20,4.39)mmol/L比4.09(3.47,4.96)mmol/L,Z=-2.082]、三酰甘油[1.20(0.78,1.86)mmol/L比1.53(1.05,1.99)mmol/L,Z=-2.343]、MoCA量表评分[21.0(20.0,22.0)分比24.0(22.0,25.0)分,Z=-9.862]均低于DMV低-中分组(均P<0.05)。其余基线资料差异均无统计学意义(均P>0.05)。多因素Logistic回归分析结果显示,较高的年龄(OR=1.181,95%CI:1.070~1.304,P=0.001)、中重度BG-EPVS(OR=2.441,95%CI:1.186~5.024,P=0.015)、较高的BG-EPVS体积(OR=4.987,95%CI:1.218~19.350,P=0.020)和较高的WMH体积(OR=1.285,95%CI:1.044~1.582,P=0.018)与较高的DMV评分相关。Spearman相关性分析结果显示,DMV评分与RSSI患者的BG-EPVS分级呈正相关(r=0.613,P<0.01),与BG-EPVS体积呈正相关(r=0.549,P<0.01),与RSSI患者的MoCA量表评分呈负相关(r=-0.449,P<0.01)。结论年龄、BG-EPVS分级、BG-EPVS体积和WMH体积与RSSI患者的DMV可见性相关;RSSI患者DMV的可见性越差,认知功能损伤越严重。展开更多
文摘In this paper, we will obtain the weak type estimates of intrinsic square func- tions including the Lusin area integral, Littlewood-Paley g-function and g^-function on the weighted Morrey spaces L^1,k （w） for 0〈k〈 1 and w ∈ A1.
文摘In this note, we consider the multipliers on weighted function spaces over totally disconnected locally compact abelian groups (Vilenkin groups). Firstly we show an (H1 ,L ) multiplier result. We also give an (Hap ,Hap) multiplier result under a similiar condition of Lu Yang type. In section 2, we obtain a result about the boundedness of multipliers on weighted Besov spaces.
文摘We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applications, we also give estimates of the es- sential norms of weighted composition operators between weighted Banach space of analytic functions and Bloch-type spaces.
基金supported by the National Natural Science Foundation of China (10901158)
文摘In this article, we study the boundedness of weighted composition operators between different vector-valued Dirichlet spaces. Some sufficient and necessary conditions for such operators to be bounded are obtained exactly, which are different completely from the scalar-valued case. As applications, we show that these vector-valued Dirichlet spaces are different counterparts of the classical scalar-valued Dirichlet space and characterize the boundedness of multiplication operators between these different spaces.
文摘Suppose T^k,l and T^k,2 are singular integrals with variable kernels and mixed homogeneity or ±I （the identity operator）. Denote the Toeplitz type operator by T^b=k=1∑^QT^k,1M^bT^k,2 where M^bf= bf. In this paper, the boundedness of Tb on weighted Morrey space are obtained when b belongs to the weighted Lipschitz function space and weighted BMO function space, respectively.
文摘In this paper we consider the Nemytskii operator, i.e., the composition operator defined by (Nf)(t)=H(t,f(t)), where H is a given set-valued function. It is shown that if the operator N maps the space of functions bounded φ1-variation in the sense of Riesz with respect to the weight function αinto the space of set-valued functions of bounded φ2-variation in the sense of Riesz with respect to the weight, if it is globally Lipschitzian, then it has to be of the form (Nf)(t)=A(t)f(t)+B(t), where A(t) is a linear continuous set-valued function and B is a set-valued function of bounded φ2-variation in the sense of Riesz with respect to the weight.
基金Supported by the National Natural Science Foundation of China(11071065 and 11171306)
文摘In this paper, several new results on the boundedness of parammetric Marcinkiewicz integrals on the weighted Hardy spaces and the weak weighted Hardy spaces are established.
基金supported by NSFC (NO. 11201003)Education Committee of Anhui Province (NO. KJ2011A138 and NO. KJ2012A133)
文摘In this paper, we will use a method of sharp maximal function approach to show the boundedness of commutator [b,TR^δ] by Bochner-Riesz operators and the function b on weighted Morrey spaces L^p,k （ω） under appropriate conditions on the weight w, where b belongs to Lipschitz space or weighted Lipschitz space.
基金supported by SQU Grant No.IG/SCI/DOMS/16/12The second author was partially supported by NSFC(11720101003)the Project of International Science and Technology Cooperation Innovation Platform in Universities in Guangdong Province(2014KGJHZ007)
文摘We characterize boundedness and compactness of products of differentiation op- erators and weighted composition operators between weighted Banach spaces of analytic functions and weighted Zygmund spaces or weighted Bloch spaces with general weights.
基金This work was supported by NSF of China(11171203,11201280)New Teacher’s Fund for Doctor Stations,Ministry of Education(20114402120003)NSF of Guangdong Province(10151503101000025,S2011010004511,S2011040004131)
文摘We characterize the boundedness and compactness of weighted composition operators on weighted Dirichlet spaces in terms of Nevanlinna counting functions and Caxleson measure.
文摘In this article, we obtain the LP-boundedness of commutators of Lipschitz functions and singular integrals with non-smooth kernels on Euclidean spaces.
文摘[b,T] denotes the commutator of generalized Calderon-Zygmund operators T with Lipschitz function b, where b∈Lip;（R;）,（0 <β≤1） and T is aθ（t）-type Calderón-Zygmund operator. The commutator [b,T] generated by b and T is defined by[b,T]f（x）=b（x）Tf（x）-T（bf）(x)=∫k（x,y）(b（x）-b（y）)f（y）dy.In this paper, the authors discuss the boundedness of the commutator [b, T] on weighted Hardy spaces and weighted Herz type Hardy spaces and prove that [b,T] is bounded from H;（ω;） to L;（ω;）, and from HK;(ω;,ω;) to K;(ω;,ω;). The results extend and generalize the well-known ones in [7].
文摘In account of the famous Cebysev inequality, a rich theory has appeared in the literature. We establish some new weighted Cebysev type integral inequalities. Our proofs are of independent interest and provide new estimates on these types of inequalities.
文摘目的探讨近期皮质下小梗死(RSSI)患者颅内深髓静脉(DMV)可见性与不同区域血管周围间隙扩大(EPVS)及认知功能的相关性。方法回顾性连续纳入南京医科大学附属常州市第二人民医院神经内科自2022年10月至2023年10月收治的RSSI患者,所有患者入院后3 d内完成MR的常规及磁敏感加权成像(SWI)序列扫描。所有RSSI患者发病7 d内进行蒙特利尔认知评估(MoCA)量表评分。对所有患者基底节区(BG)和半卵圆中心区的EPVS进行分级评估和体积测量,使用DMV视觉评分对患者SWI幅度图或最小强度投影图上的DMV可见性进行评估,并将患者分为可见性较高的DMV低-中分组(评分0~12分,104例)及可见性较低的DMV高分组(评分13~18分,47例),采用单因素分析比较两组患者的临床和影像学资料,采用多因素Logistic回归和Spearman相关分析方法分析DMV可见性与BG-EPVS分级及体积的关系以及其与患者认知功能的关系。结果共纳入RSSI患者151例,平均年龄(69±10)岁,其中男92例(60.9%),女59例(39.1%)。DMV高分组RSSI患者的年龄[(76±5)岁比(65±10)岁,t=-10.875]、高血压病患者比例[78.7%(37/47)比54.8%(57/104),χ^(2)=7.879]、BG-EPVS分级、BG-EPVS体积[5.67(5.30,5.81)ln mm 3比4.61(3.66,5.30)ln mm 3,Z=-6.772]、脑白质高信号体积[7.67(6.23,8.43)ln mm 3比4.31(3.53,5.89)ln mm 3,Z=-6.501]均明显高于DMV低-中分组,差异均有统计学意义(均P<0.05)。DMV高分组RSSI患者的总胆固醇[3.74(3.20,4.39)mmol/L比4.09(3.47,4.96)mmol/L,Z=-2.082]、三酰甘油[1.20(0.78,1.86)mmol/L比1.53(1.05,1.99)mmol/L,Z=-2.343]、MoCA量表评分[21.0(20.0,22.0)分比24.0(22.0,25.0)分,Z=-9.862]均低于DMV低-中分组(均P<0.05)。其余基线资料差异均无统计学意义(均P>0.05)。多因素Logistic回归分析结果显示,较高的年龄(OR=1.181,95%CI:1.070~1.304,P=0.001)、中重度BG-EPVS(OR=2.441,95%CI:1.186~5.024,P=0.015)、较高的BG-EPVS体积(OR=4.987,95%CI:1.218~19.350,P=0.020)和较高的WMH体积(OR=1.285,95%CI:1.044~1.582,P=0.018)与较高的DMV评分相关。Spearman相关性分析结果显示,DMV评分与RSSI患者的BG-EPVS分级呈正相关(r=0.613,P<0.01),与BG-EPVS体积呈正相关(r=0.549,P<0.01),与RSSI患者的MoCA量表评分呈负相关(r=-0.449,P<0.01)。结论年龄、BG-EPVS分级、BG-EPVS体积和WMH体积与RSSI患者的DMV可见性相关;RSSI患者DMV的可见性越差,认知功能损伤越严重。
