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Boundedness of the Commutator of Marcinkiewicz Integral with Rough variable kernel

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Acta Mathematica Sinica,English Series 2009年第6期25卷 983-1000页

作者： Yan Ping CHEN Department of Mathematics and Mechanics Applied Science School University of Science and Technology of Beijing Beijing 100083 P. R. China

In this paper the author proves that the commutator of the Marcinkiewicz integral operator with rough variable kernel is bounded from the homogeneous Sobolev space Lγ^2（R^n） to the Lebesgue space L^2（R^n）, which ... 详细信息

关键词： commutator Marcinkiewicz integral variable kernel BMO Sobolev space spherical harmonic function

Weighted Estimates of variable kernel Fractional Integral and Its Commutators on Vanishing Generalized Morrey Spaces with variable Exponent

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Chinese Annals of Mathematics,Series B 2021年第3期42卷 451-470页

作者： Xukui SHAO Shuangping TAO School of Mathematics and Statistics LongDong UniversityQingyang 745000GansuChina School of Mathematics and statistics Northwest Normal UniversityLanzhou 730070China Corresponding author.School of Mathematics and Statistics Northwest Normal UniversityLanzhou 730070China

In this paper,the authors obtain the boundedness of the fractional integral operators with variable kernels on the variable exponent generalized weighted Morrey spaces and the variable exponent vanishing generalized w... 详细信息

关键词： Fractional integral Commutator variable kernel Vanishing generalized weighted Morrey space with variable exponent BMO space

Boundedness for the Singular Integral with variable kernel and Fractional Differentiation on Weighted Morrey Spaces

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Analysis in Theory and Applications 2016年第3期32卷 205-214页

作者： Chao Xue Kai Zhu Yanping Chen Department of Applied Mathematics University of Science and Technology Beijing School of Mathematical Sciences Beijing Normal University

Let T be the singular integral operator with variable kernel, T＊ be the adjoint of T and T# be the pseudo-adjoint of T. Let TIT2 be the product of T1 and T2, T1 o T2 be the pseudo product of T1 and T2. In this paper, we establish the boundedness for commutators of these operators and the fractional differentiation operator D^γ on the weighted Morrey spaces.

关键词： Singular integral variable kernel fractional differentiation BMO Sobolev space weighted Morrey spaces

The Boundedness of Fractional Integral with variable kernel on variable Exponent Herz-Morrey Spaces

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Journal of Applied Mathematics and Physics 2016年第4期4卷 787-795页

作者： Afif Abdalmonem Omer Abdalrhman Shuangping Tao College of Mathematics and Statistics Northwest Normal University Lanzhou China Faculty of Science University of Dalanj Dalanj Sudan College of Education Shendi University Shendi Sudan

In this paper, we study the boundedness of the fractional integral with variable kernel. Under some assumptions, we prove that such kind of operators is bounded from the variable exponent Herz-Morrey spaces to the var... 详细信息

关键词： Fractional Integral variable kernel variable Exponent Herz-Morrey Spaces

Boundedness of Fractional Integral with variable kernel and Their Commutators on variable Exponent Herz Spaces

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Applied Mathematics 2016年第10期7卷 1165-1182页

In this paper, we study the boundedness of the fractional integral operator and their commutator on Herz spaecs with two variable exponents . By using the properties of the variable exponents Lebesgue spaces, the boundedness of the fractional integral operator and their commutator generated by Lipschitz function is obtained on those Herz spaces.

关键词： Fractional Integral variable kernel Commutator variable Exponent Lipschitz Space Herz Spaces

Hypersingular parameterized Marcinkiewicz integrals with variable kernels on Sobolev and Hardy-Sobolev spaces

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Applied Mathematics(A Journal of Chinese Universities) 2008年第4期23卷 420-430页

作者： CHEN Jie-cheng YU Xiao ZHANG Yan-dan WANG Hui Department of Mathematics Zhejiang University Hangzhou 310027 China

Let α≥ 0 and 0 〈 ρ ≤ n/2, the boundedness of hypersingular parameterized Marcinkiewicz integrals μΩ,α^ρ with variable kernels on Sobolev spaces Lα^ρ and HardySobolev spaces Hα^ρ is established.

关键词： parameterized Marcinkiewicz integral variable kernel Hardy-Sobolev space L^α-Dini condition

Generalized Commutators for Marcinkiewicz Type Integrals with variable kernels

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Acta Mathematicae Applicatae Sinica 2011年第3期27卷 471-480页

作者： Hui-xia Mo Shan-zhen Lu School of Science Beijing University of Post and Telecommunications Beijing 100876 China School of Mathematical Sciences Beijing Normal University Beijing 100875 China

Let A be a function with derivatives of order m and D γ A ∈■β （0 〈 β 〈 1, ｜γ｜ = m）. The authors in the paper prove that if Ω（x, z） ∈ L ∞ （R n ） × L s （S n 1 ）（s ≥ n/（n β）） is homogenous of... 详细信息

Let A be a function with derivatives of order m and D γ A ∈■β （0 〈 β 〈 1, ｜γ｜ = m）. The authors in the paper prove that if Ω（x, z） ∈ L ∞ （R n ） × L s （S n 1 ）（s ≥ n/（n β）） is homogenous of degree zero and satisfies the mean value zero condition about the variable z, then both the generalized commutator for Marcinkiewicz type integral μ A Ω and its variation μ A Ω are bounded from L p （R n ） to L q （R n ）, where 1 〈 p 〈 n/β and 1/q = 1/p β/n. The authors also consider the boundedness of μ A Ω and its variation μ A Ω on Hardy spaces.

关键词： Marcinkiewicz integral variable kernel Lipschitz space Hardy space

A note on parameterized Marcinkiewicz integrals with variable kernels

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Applied Mathematics(A Journal of Chinese Universities) 2009年第3期24卷 315-320页

作者： WANG Hui ZHANG Chun-jie Department of Mathematics Zhejiang University Hangzhou 310027 China Department of Mathematics Hangzhou Dianzi University Hangzhou 310018 China

In this paper,the parameterized Marcinkiewicz integrals with variable kernels defined by μΩ^ρ（f）（x）=（∫0^∞│∫│1-y│≤t Ω（x,x-y）/│x-y│^n-p f（y）dy│^2dt/t1＋2p）^1/2 are *** is proved that if Ω∈ L∞（R^n） × L^r（S^n-1）（r〉（n-n1p＇/n） is an odd function in the second variable y,then the operator μΩ^ρ is bounded from L^p（R^n） to L^p（R^n） for 1 〈 p ≤ max{（n＋1）/2,2}.It is also proved that,if Ω satisfies the L^1-Dini condition,then μΩ^ρ is of type（p,p） for 1 〈 p ≤ 2,of the weak type（1,1） and bounded from H1 to L1.

关键词： parameterized Marcinkiewicz integral variable kernel rotation method

THE FRACTIONAL MULTILINEAR SINGULAR INTEGRAL WITH variable kernelS ON HARDY SPACES

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Analysis in Theory and Applications 2006年第1期22卷 81-90页

作者： Zheng Yang Jiacheng Lan Lishui University China

The authors discuss Lipschitz boundedness for a class of fractional multilinear operators with variable kernels. It is obtained that these operators are both Lipschitz bounded from L^p to H^q.

关键词： variable kernel multilinear fractional integral space Aβ (R^n) Hardy space