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Multilinear Singular Integrals with rough kernel

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Acta Mathematica Sinica,English Series 2003年第1期19卷 51-62页

作者： ShanZhenLU HuoXiongWU PuZHANG DepartmentofMathermatics BeijngNormalUniversityBeijing100875 DepartmentofMathermatics ZhejiangUniversity(atXixiCampus)Hangzhou310028

For a class of multilinear singular integral operators TA,$$T_A f\left( x \right) = \int {_{\Ropf^n} } {{\Omega \left( {x - y} \right)} \over {\left| {x - y} \right|^{n + m - 1} }}R_m \left( {A;x,y} \right)f\left( y \right)dy,$$where Rm (A; x, y) denotes the m-th Taylor series remainder of A at x expanded about y, A has derivatives of order m m 1 in $\dot \Lambda_\beta $(0 < # < 1), OHgr;(x) ] L^s(S^nm1)($s \ge {n \over {n - \beta }}$) is homogeneous of degree zero, the authors prove that TA is bounded from L^p(A^n) to L^q) (A^n) (${1 \over p} - {1 \over q} = {\beta \over n},\,1 < p < {n \over \beta }$) and from L^1 (A^n) to L^n/(nm#), ^X (A^n) with the bound $C\sum\nolimits_{\left| \gamma \right| = m - 1} {} \left\|\left\| {D^\gamma A} \right\|\right\|_{\dot \Lambda_\beta} $. And if Q has vanishing moments of order m m 1 and satisfies some kinds of Dini regularity otherwise, then TA is also bounded from L^p (A^n) to ${\dot F}^{\beta,\infty}_p$ (A^n)(1 < s' < p < X) with the bound $C\sum\nolimits_{\left| \gamma \right| = m - 1} {} \left\| \left\|{D^\gamma A} \right\|\right\|_{\dot \Lambda _\beta } $.

关键词： Multilinear operator Singular integral Lipschitz spaces Triebel Lizorkin spaces rough kernel

Parabolic Littlewood-Paley g-Function with rough kernel

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Acta Mathematica Sinica,English Series 2008年第12期24卷 2049-2060页

作者： Qing Ying XUE Yong DING Kozo YABUTA School of Mathematical Sciences Laboratory of Mathematics and Complex Systems( BNU) Ministry of Education China Beijing Normal University Beijing 100875 P. R. China School of Science and Technology Kwansei Gakuin University Gakuen 2-1 Sanda 669-1337 Japan

In this note, we give the L^p （1 〈 p 〈∞） boundedness of the parabolic Littlewood Paley g-function with rough kernel.

关键词： parabolic Littlewood-Paley g-function mixed homogeneity spaces rough kernel

Weighted Boundedness for a Class of rough Multilinear Operators

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Acta Mathematica Sinica,English Series 2001年第3期17卷 517-526页

作者： Yong DING Shan Zhen LU Department of Mathematics,Beijing Normal University,Beijing 100875,P.R.China E-mail:dingy@*** lusz@*** Department of Mathematics Beijing Normal University Beijing 100875 P. R. China

In this paper we give the (L^p(ω~p),L^q(ω~q)) boundedness for a class of multilinear operators, which is similar to the higher-order commutator for the rough fractional integral.In our results the kernel function is... 详细信息

关键词： Multilinear operator Fractional integral rough kernel BMO A(p,q) weight

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

Weighted boundedness of some integral operators on weighted λ-central Morrey space

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Applied Mathematics(A Journal of Chinese Universities) 2016年第3期31卷 331-342页

作者： YU Xiao ZHANG Hui-hui ZHAO Guo-ping Department of Mathematics Shangrao Normal University School of Applied Mathematics Xiamen University of Technology Department of Mathematics Zhejiang University

In this paper, the authors prove the weighted boundedness of singular integral and fractional integral with a rough kernel on the weighted λ-central Morrey space. Moreover, the weighted estimate for commutators of si... 详细信息

关键词： weighted central-Morrey space weighted central-BMO space rough kernel commutator

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.

On rough Marcinkiewicz Integrals along Surfaces

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Acta Mathematica Sinica,English Series 2010年第4期26卷 717-730页

作者： Huo Xiong WU Jian Kai XU School of Mathematical Sciences Xiamen University Xiamen 361005 P. R. China

In this paper, the authors establish the LP-mapping properties of certain classes of Marcinkiewicz integral operators along surfaces with rough kernels. The results in this paper essentially extend as well as improve ... 详细信息

关键词： Marcinkiewicz integrals surfaces maximal operator Hardy space rough kernel

rough MARCINKIEWICZ INTEGRALS ASSOCIATED TO SURFACES OF REVOLUTION ON PRODUCT DOMAINS

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Acta Mathematica Scientia 2009年第2期29卷 294-304页

作者：伍火熊许建开 School of Mathematical Sciences Xiamen University

In this article, certain Marcinkiewicz integral operators associated to surfaces of revolution on product domains were studied. The Lp boundedness for these operators are established under some rather weak conditions ... 详细信息

关键词： Marcinkiewicz integral product domain surfaces of revolution rough kernel

Boundedness of commutators on homogeneous Herz spaces

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Science China Mathematics 1998年第10期41卷 1023-1033页

作者：陆善镇唐林杨大春 Department of Mathematics Beijing Normal Univeraity Beijing 100875China Department of Mathematics Xinjiang Univeraty Xinjiang 830046China Department of Mathematics Beijing Normal Univeraity Beijing 100875China

The boundedness on homogeneous Herz spaces is established fo r a large class of linear commutators generated by BMO(R+n) functions and linear operators of rough kernels which include the CaldernZygmund oper ators an... 详细信息

关键词： Herz space power weight commutator BMO(R^(n))function singular integral rough kernel