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Boundedness of marcinkiewicz integral with rough kernel on Triebel-Lizorkin spaces

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Frontiers of Information Technology & Electronic Engineering 2015年第8期16卷 654-657页

作者： Chun-jie ZHANG Fang-fang REN Yu-huai ZHANG Gui-lian GAO Department of Mathematics Hangzhou Dianzi University

This paper is a continuation of our previous work （Zhang and Chen, 2010b）. Following the same generalsteps of the proof there, we make essential improvement on our previous theorem by recalculating a key inequality. Our result shows that the marcinkiewicz integral, with a bounded radial function in its kernel, is still bounded on the Triebel-Lizorkin space.

关键词： marcinkiewicz integral Triebel-Lizorkin spaces

Boundedness of Some marcinkiewicz integral Operators Related to Higher Order Commutators on Hardy Spaces

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Acta Mathematica Sinica,English Series 2006年第1期22卷 105-114页

作者： Shan Zhen LU Li Fang XU Department of Mathematics Beijing Normal University Beijing 100875 P. R. China

In this paper, the authors study the boundedness properties of μΩ↑m,b generated by the function b ∈Lipβ（R^n）（0 〈β≤ 1/m） and the marcinkiewicz integrals operator μΩ. The boundednesses are established on t... 详细信息

关键词： marcinkiewicz integral Higher order commutator Lipshcitz space Hardy type space Herz space

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

Commutators of marcinkiewicz integral with Rough Kernels on Sobolev Spaces

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Acta Mathematica Sinica,English Series 2011年第7期27卷 1345-1366页

作者： Yan Ping CHEN Yong DING Xin Xia WANG Department of Mathematics and Mechanics School of Applied ScienceUniversity of Science and Technology of Beijing Beijing 100083 P. R. China School of Mathematical Sciences Beijing Normal UniversityLaboratory of Mathematics and Complex Systems (BNU) Ministry of Education Beijing 100875 P. R. China The College of Mathematics and Systems Science Xinjiang University U~'umqi 830046 P. R. China

In this paper, the authors give the boundedness of the commutator [b,μΩ,γ] from the homogeneous Sobolev space LP（R^n） to the Lebesgue space L^p（R^n） for 1 〈 p 〈 ∞, where μΩ,γ denotes the marcinkiewicz integral with rough hypersingular kernel defined by μΩ,γf（x）=（∫0^∞｜∫｜x-y｜≤tΩ（x-y）/｜x-y｜^n-1f（y）dy｜^2dt/t^3＋2γ）^1/2,with Ω∈L^1（S^n-1）for 0〈γ〈min（n/2,n/p）or Ω∈L（log＋L）^β（S^n-1）for｜1-2/p｜〈β〈1（0〈γ〈n/2）,respectively.

关键词： marcinkiewicz integral commutator rough kernel Sobolev space Bony paraproduct

A Note on the Generalized marcinkiewicz integral Operators with Rough Kernels

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Acta Mathematica Sinica,English Series 2012年第12期28卷 2395-2406页

作者： Yu Rong WU Huo Xiong WU School of Mathematical Sciences Xiamen University School of Mathematical Sciences Fudan University

In this paper, we study the generalized marcinkiewicz integral operators MΩ,r on the product space Rn ×Rm. Under the condition that Ω is a function in certain block spaces, which is optimal in some senses, the boun... 详细信息

关键词： marcinkiewicz integral Triebel-Lizorkin space vector-valued multiplier theorem rough kernel product space

Weighted Estimates for Multilinear Commutators of marcinkiewicz integral

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Acta Mathematica Sinica,English Series 2008年第8期24卷 1387-1400页

作者： Pu ZHANG Department of Mathematics Mudanjiang Teachers College Mudanjiang 157012 P. R. China

Let μ be the n-dimensional marcinkiewicz integral and μb the multilinear commutator of μ. In this paper, the following weighted inequalities are proved for ω ∈ A∞ and 0 〈 p 〈 ∞,｜｜μ（f）｜｜LP（ω）≤C｜Mf｜LP（ω） and ｜｜μb（f）｜｜LP（ω）≤C｜｜ML（log L）^1/r f｜｜LP（ω）.The weighted weak L（log L）^1/r -type estimate is also established when p=1 and ω∈A1.

关键词： marcinkiewicz integral multilinear commutator sharp function Ap weights

Boundedness of marcinkiewicz integral on Triebel-Lizorkin spaces

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Applied Mathematics(A Journal of Chinese Universities) 2010年第1期25卷 48-54页

作者： ZHANG Chun-jie CHEN Jie-cheng College of Science Hanzhou Dianzi University Hangzhou 310018 China Department of Mathematics Zhejiang University Hangzhou 310027 China

In this paper, we prove the Triebel-Lizorkin boundedness for the marcinkiewicz integral with rough kernel. The method we apply here enables us to consider more general operators.

关键词： marcinkiewicz integral Triebel-Lizorkin spaces rough kernel singular integral.

BOUNDEDNESS OF GENERALIZED marcinkiewicz integral ON THE H^p-SOBOLEV SPACES

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Applied Mathematics(A Journal of Chinese Universities) 2004年第4期19卷 399-404页

作者： JiangLiya JiaHouyu XuHan Dept.ofMath. ZhejiangUniv.Hangzhou310028China. Dept.ofInform.andComput.Sci..ZhejiangUniversityofSciences Hangzhou310018China.

In this paper, the general marcinkiewicz integral operator μ Ω,α on the H p Sobolev spaces under the proper condition of kernel Ω(x′) is considered. It is obtained that μ Ω,α is bounded from H p ... 详细信息

关键词： marcinkiewicz integral Triebel-Lizorkin space atomic decomposition.

Boundedness of marcinkiewicz integral on Weighted Herz Spaces

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Chinese Quarterly Journal of Mathematics 2008年第2期23卷 228-234页

作者： XIE Ru-long SHU Li-sheng College of Mathematics and Computer Science Anhui Normal University Wuhu 241000 China Department of Mathematics Ghaohu College Chaohu 238000 China

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