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Boundedness of Marcinkiewicz Integral on Weighted Herz Spaces
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作者 XIE Ru-long SHU Li-sheng 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2008年第2期228-234,共7页
In this paper, it is proved that the Marcinkiewicz integral operator μΩ is bounded on Kq^α,p(ω1;ω2).
关键词 Marcinkiewicz integral weighted herz space A1 weight
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Weak Type Estimates for Intrinsic Square Functions on Weighted Morrey Spaces 被引量:2
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作者 Hua Wang 《Analysis in Theory and Applications》 2013年第2期104-119,共16页
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
关键词 Intrinsic square function weighted Morrey space Ap weight.
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Boundedness of Marcinkiewicz Integrals in Weighted Variable Exponent Herz-Morrey Spaces 被引量:2
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作者 XIAO DAN SHU LI-SHENG Ji You-qing 《Communications in Mathematical Research》 CSCD 2018年第4期371-382,共12页
In this paper, under natural regularity assumptions on the exponent function, we prove some boundedness results for the functions of Littlewood-Paley, Lusin and Marcinkiewicz on a new class of generalized Herz-Morrey ... In this paper, under natural regularity assumptions on the exponent function, we prove some boundedness results for the functions of Littlewood-Paley, Lusin and Marcinkiewicz on a new class of generalized Herz-Morrey spaces with weight and variable exponent, which essentially extend some known results. 展开更多
关键词 Marcinkiewicz integral variable exponent Muckenhoupt weight herz-Morrey space
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A STUDY ON THE WEIGHT FUNCTION OF THE MOVING LEAST SQUARE APPROXIMATION IN THE LOCAL BOUNDARY INTEGRAL EQUATION METHOD 被引量:4
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作者 Long Shuyao Hu De’an (Department of Engineering Mechanics,Hunan University,Changsha 410082,China) 《Acta Mechanica Solida Sinica》 SCIE EI 2003年第3期276-282,共7页
The meshless method is a new numerical technique presented in recent years.It uses the moving least square(MLS)approximation as a shape function.The smoothness of the MLS approximation is determined by that of the bas... The meshless method is a new numerical technique presented in recent years.It uses the moving least square(MLS)approximation as a shape function.The smoothness of the MLS approximation is determined by that of the basic function and of the weight function,and is mainly determined by that of the weight function.Therefore,the weight function greatly affects the accuracy of results obtained.Different kinds of weight functions,such as the spline function, the Gauss function and so on,are proposed recently by many researchers.In the present work,the features of various weight functions are illustrated through solving elasto-static problems using the local boundary integral equation method.The effect of various weight functions on the accuracy, convergence and stability of results obtained is also discussed.Examples show that the weight function proposed by Zhou Weiyuan and Gauss and the quartic spline weight function are better than the others if parameters c and α in Gauss and exponential weight functions are in the range of reasonable values,respectively,and the higher the smoothness of the weight function,the better the features of the solutions. 展开更多
关键词 weight function meshless methods local boundary integral equation method moving least square approximation
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BOUNDEDNESS OF COMMUTATORS FOR MARCINKIEWICZ INTEGRALS ON WEIGHTED HERZ-TYPE HARDY SPACES 被引量:1
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作者 Cuilan Wu 《Analysis in Theory and Applications》 2011年第4期365-376,共12页
In this paper, the authors study the boundedness of the operator μ^bΩ, the commutator generated by a function b ∈Lipβ (R^n) (0 〈β 〈 1) and the Marcinkiewicz integral μΩ on weighted Herz-type Hardy spaces.
关键词 Marcinkiewicz integral COMMUTATOR weighted herz space Hardy space
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BOUNDEDNESS OF COMMUTATORS OF GENERALIZED FRACTIONAL INTEGRAL OPERATORS ON WEIGHTED HERZ-TYPE HARDY SPACES 被引量:1
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作者 Aiwen Sun Lisheng Shu 《Analysis in Theory and Applications》 2010年第2期101-109,共9页
In this paper, we study the boundedness of higher order commutators of gen- eralized fractional integral operators on weighted Lp spaces and Herz-type Hardy spaces.
关键词 generalized fractional integral COMMUTATOR weighted herz-type Hardy space atom
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BOUNDEDNESS OF MARCINKIEWICZ INTEGRAL ON THE WEIGHTED HERZ-TYPE HARDY SPACES
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作者 Lejin Xu 《Analysis in Theory and Applications》 2006年第1期56-64,共9页
In this paper, we discuss the boundedness of Marcinkiewicz integral μΩ with homogeneous kernel on the weighted Herz-type Hardy spaces, and prove that μΩ is bounded from HKq^a、P(ω1;ω2) into Kq^a、p (ω1; ω2).
关键词 Marcinkiewicz integral L^r-Dini condition weighted herz-type Hardy spaces
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Boundedness of parammetric Marcinkiewicz integrals on weighted Hardy spaces
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作者 SHI Xian-liang SUN Jie 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2015年第3期253-262,共10页
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.
关键词 parammetric Marcinkiewicz integral weight function weighted Hardy space weak weighted Hardy space
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Multilinear Fractional Integrals and Commutators on Generalized Herz Spaces
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作者 Yueshan Wang Yuexiang He 《Analysis in Theory and Applications》 CSCD 2016年第2期103-121,共19页
Suppose b= (b1,…,bm) E (BMO)^m, Iα,m^∏b is the iterated commutator of b and the m-linear multilinear fractional integral operator Iα,m. The purpose of this paper is to discuss the boundedness properties of Iα... Suppose b= (b1,…,bm) E (BMO)^m, Iα,m^∏b is the iterated commutator of b and the m-linear multilinear fractional integral operator Iα,m. The purpose of this paper is to discuss the boundedness properties of Iα,m and Iα,m^∏b on generalized Herz spaces with general Muckenhoupt weights. 展开更多
关键词 Multilinear fractional integral generalized herz space COMMUTATOR Muckenhoupt weight.
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Toeplitz Type Operator Associated to Singular Integral Operator with Variable Kernel on Weighted Morrey Spaces 被引量:1
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作者 Yuexiang He Yueshan Wang 《Analysis in Theory and Applications》 CSCD 2016年第1期90-102,共13页
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
关键词 Toeplitz type operator singular integral operator variable Calderon-Zygmund kernel weighted BMO function weighted Lipschitz function weighted Morrey space.
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Multilinear singular and fractional integrals on weighted Hardy spaces
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作者 ZHANG Pu LAN Jia-cheng 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2009年第2期214-220,共7页
In this paper the boundedness properties of multilinear singular and fractional integrals on the weighted Hardy spaces are studied.
关键词 multilinear singular integral multilinear fractional integral Lipschitz function L^r-Dini condition weighted Hardy space
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Singular Integrals and Weighted Triebel-Lizorkin and Besov Spaces of Arbitrary Number of Parameters 被引量:7
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作者 Guo Zhen LU Yue Ping ZHU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2013年第1期39-52,共14页
Though the theory of Triebel-Lizorkin and Besov spaces in one-parameter has been developed satisfactorily, not so much has been done for the multiparameter counterpart of such a theory. In this paper, we introduce the... Though the theory of Triebel-Lizorkin and Besov spaces in one-parameter has been developed satisfactorily, not so much has been done for the multiparameter counterpart of such a theory. In this paper, we introduce the weighted Triebel-Lizorkin and Besov spaces with an arbitrary number of parameters and prove the boundedness of singular integral operators on these spaces using discrete Littlewood-Paley theory and Calderon's identity. This is inspired by the work of discrete Littlewood- Paley analysis with two parameters of implicit dilations associated with the flag singular integrals recently developed by Han and Lu [12]. Our approach of derivation of the boundedness of singular integrals on these spaces is substantially different from those used in the literature where atomic decomposition on the one-parameter Triebel-Lizorkin and Besov spaces played a crucial role. The discrete Littlewood-Paley analysis allows us to avoid using the atomic decomposition or deep Journe's covering lemma in multiparameter setting. 展开更多
关键词 Singular integrals multiparameter weighted Triebel-Lizorkin spaces multiparameter weighted Besov spaces discrete Littlewood-Paley analysis discrete Calderon identity vector-valued maximal functions
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Boundedness of commutators on homogeneous Herz spaces 被引量:12
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作者 陆善镇 唐林 杨大春 《Science China Mathematics》 SCIE 1998年第10期1023-1033,共11页
The boundedness on homogeneous Herz spaces is established for a large class of linear commutators generated by BMO(R n ) functions and linear operators of rough kernels which include the Calderón-Zygmund operator... The boundedness on homogeneous Herz spaces is established for a large class of linear commutators generated by BMO(R n ) functions and linear operators of rough kernels which include the Calderón-Zygmund operators and the Ricci-Stein oRfiUatory singular integrals with rough kernels. 展开更多
关键词 herz space power weight COMMUTATOR BMO(R^(n))function singular integral rough kernel
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Commutators of Lipschitz Functions and Singular Integrals with Non-Smooth Kernels on Euclidean Spaces
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作者 Hung Viet Le 《Analysis in Theory and Applications》 CSCD 2016年第2期135-148,共14页
In this article, we obtain the LP-boundedness of commutators of Lipschitz functions and singular integrals with non-smooth kernels on Euclidean spaces.
关键词 COMMUTATORS singular integrals maximal functions sharp maximal functions muck-enhoupt weights Lipschitz spaces.
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BOUNDEDNESS OF COMMUTATORS OF FRACTIONAL INTEGRATI ON ONHERZ-TYPE SPACES 被引量:1
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作者 刘宗光 《Acta Mathematica Scientia》 SCIE CSCD 2000年第4期461-470,共10页
This paper establishes some strong type and weak type estimates for commutator [b,I1] on Herz-type spaces, where b E BMO(Rn) and I1 is a fractional integration with O < l < n.
关键词 herz space weak herz space herz-type Hardy space fractional integration BMO(Rn) function COMMUTATOR
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AREA INTEGRAL FUNCTIONS FOR SECTORIAL OPERATORS ON L^p SPACES 被引量:1
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作者 陈泽乾 孙牧 《Acta Mathematica Scientia》 SCIE CSCD 2014年第3期739-747,共9页
Area integral functions are introduced for sectorial operators on L^p-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on L^p spaces. This follows that the re... Area integral functions are introduced for sectorial operators on L^p-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on L^p spaces. This follows that the results of Cowling, Doust, McIntosh, Yagi, and Le Merdy on H^∞ functional calculus of seetorial operators on LP-spaces hold true when the square functions are replaced by the area integral functions. 展开更多
关键词 Sectorial operator H^∞ functional calculus area integral function square function L^p space
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Boundedness for Multilinear Commutators of Marcinkiewicz Integral on Morrey-Herz Spaces with Non Doubling Measures
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作者 Jianglong Wu Qingguo Liu 《Analysis in Theory and Applications》 2013年第1期62-71,共10页
In this paper, the authors establish the boundedness of multilinear commutators generated by a Marcinkiewicz integral operator and a RBMO(μ) function on homogeneous Morrey-Herz spaces with non doubling measures.
关键词 Marcinkiewicz integral COMMUTATOR Morrey-herz space non doubling measure RBMO function.
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某类次线性算子在加权变指数Herz空间上的有界性
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作者 王英杰 赵睿刚 汤灿琴 《湖南文理学院学报(自然科学版)》 CAS 2023年第2期1-6,14,共7页
利用加权变指数Herz空间的等价定义,获得了满足某类尺寸条件及L^(p(·))(ω)有界性假设下的次线性算子及次线性分数次积分算子在加权Herz空间K_(p(·),q)^(a(·))(ω)上的有界性。
关键词 次线性算子 次线性分数次积分算子 加权herz型空间 变指数
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可变核Marcinkiewicz积分交换子在Herz型Hardy空间上的有界性 被引量:11
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作者 陶祥兴 位瑞英 《数学物理学报(A辑)》 CSCD 北大核心 2009年第6期1508-1517,共10页
该文研究由可变核Marcinkiewicz积分和Lip_β(R^n)(0<β≤1)函数生成的交换子μ_(Ω,b).证明了当可变核Ω∈L~∞(R^n)×L^r(S^(n-1))(r≥1)时,交换子μ_(Ω,b)从Herz型Hardy空间到Herz空间的有界性.同时建立了参数型Marcinkiewic... 该文研究由可变核Marcinkiewicz积分和Lip_β(R^n)(0<β≤1)函数生成的交换子μ_(Ω,b).证明了当可变核Ω∈L~∞(R^n)×L^r(S^(n-1))(r≥1)时,交换子μ_(Ω,b)从Herz型Hardy空间到Herz空间的有界性.同时建立了参数型Marcinkiewicz积分的交换子μ_(Ω,b)~ρ在Herz型Hardy空间上的有界性. 展开更多
关键词 交换子 可变核Marcinkiewicz积分 herz型HARDY空间 L^τ γ-Dini条件 Lipβ函数
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加权Herz空间上交换子的有界性 被引量:3
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作者 江寅生 刘明菊 《应用泛函分析学报》 CSCD 2001年第1期52-59,共8页
旨在建立一大类由 BMO函数和线性算子所生成交换子在加权 Herz空间上的有界性 ,这些线性算子包括 Calderón-Zygmund奇异积分算子 ,带有粗糙核的 R.Fefferman型奇异积分算子和带有粗糙核的
关键词 herz空间 交换子 BMO函数 奇异积分 粗糙核 有界性 奇异积分算子 线性算子
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