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weighted norm INEQUALITIES FOR THE COMMUTATORS OF MULTILINEAR SINGULAR INTEGRAL OPERATORS

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Acta Mathematica Scientia 2011年第3期31卷 749-764页

作者： Hu Guoen Zhu Yueping Department of Applied Mathematics Zhengzhou Information Science and Technology Institute Zhengzhou 450002 China School of Science Nantong University Nantong 226007 China

In this paper, the authors consider the weighted estimates for the commutators of multilinear Calderón-Zygmund *** introducing an operator which shifts the commutation, and establishing the weighted estimates for this new operator, the authors prove that, if p_1 ∈ （1,∞）, p_2,…,p_m ∈（1,∞], p ∈ （0,∞） with 1/p =Σ1≤k≤ m 1/pk, then for any weight w, the commutators of m-linear Galderón-Zygmund operator are bounded from L P1（R n,M_l（logL） σw）× p2（Rn,M~w）×...×Lpm（Rn,Mw） to Lp（Rn,w）with σ to be a constant depending only on p_1 and the order of commutator

关键词： multilinear Calderón-Zygmund operator weighted norm inequality commutator Caldern-Zygmund decomposition

weighted norm Inequalities with General Weights for the Commutator of Calderón

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Acta Mathematica Sinica,English Series 2013年第3期29卷 505-514页

作者： Guo En HU Yue Ping ZHU Department of Applied Mathematics Zhengzhou Information Science and Technology Institute School of Science Nantong University

In this paper, by a sharp function estimate and an idea of Lerner, the authors establish some weighted estimates for the m-multilinear integral operator which is bounded from L1 （Rn） ×..…… L1 （Rn） to L1/m,∞（Rn）, and the associated kernel K（x; yl,.. , Ym） enjoys a regularity on the variable x. As an application, weighted estimates with general weights are given for the commutator of CalderSn.

关键词： Approximation to the identity weighted norm inequality singular integral operator max-imal operator non-smooth kernel

Some weighted norm Inequalities on Manifolds

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Chinese Annals of Mathematics,Series B 2018年第6期39卷 1001-1016页

作者： Shiliang ZHAO School of Mathematical Sciences Fudan University

Let M be a complete non-compact Riemannian manifold satisfying the volume doubling property and the Gaussian upper bounds. Denote by A the Laplace-Beltrami operator and by V the Riemannian gradient. In this paper, the author proves the weighted reverse inequality ｜｜Δ^1/2f｜｜L^p（w）×C｜｜｜Δ↓｜｜｜L^p（w）, for some range ofp determined by M and w. Moreover, a weak type estimate is proved when p = 1. Some weighted vector-valued inequalities are also established.

关键词： weighted norm inequality Poincare inequality Riesz transform.

weighted norm Inequalities for a Class of Multilinear Singular Integral Operators

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Journal of Mathematical Research with Applications 2014年第2期34卷 168-174页

作者： Rongqian WANG Basic Education and Scientific Department Henan Polytechnic Institute

In this paper, weighted estimates with general weights are established for the multilinear singular integral operator defined by TAf(x) = p. ***Ω(x- y)|x- y|n+1 A(x)- A(y)- A(y)(x- y) f(y)dy,where Ω is homogeneous of degree zero, has vanishing moment of order one, and belongs to Lipγ(Sn-1) with γ∈(0, 1], A has derivatives of order one in BMO(Rn).

关键词： multilinear singular integral operator weighted norm inequality sharp function estimate BMO.

weighted estimates for the multilinear singular integral operators with non-smooth kernels

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Science China Mathematics 2011年第3期54卷 587-602页

作者： HU GuoEn1 & LU ShanZhen2 1Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou 450002, China 2Department of Mathematics, Beijing normal University, Beijing 100875, China Department of Applied Mathematics Zhengzhou Information Science and Technology Institute Zhengzhou China Department of Mathematics Beijing Normal University Beijing China

In this paper, by sharp function estimates and certain weak type endpoint estimates, the authors establish some weighted norm inequalities with Ap weights for the multilinear singular integral operators with non-smoot... 详细信息

关键词： approximation to the identity weighted norm inequality singular integral operator non-smooth kernel Calderón-Zygmund decomposition

Bilinear Fourier Multiplier Operator on Morrey Spaces

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Journal of Mathematical Research with Applications 2014年第6期34卷 703-712页

作者： Yulan JIAO School of Science University of Information Engineering

In this paper, by establishing a result concerning the mapping properties for bi(sub)linear operators on Morrey spaces, and the weighted estimates with general weights for the bilinear Fourier multiplier, the author establishes some results concerning the behavior on the product of Morrey spaces for bilinear Fourier multiplier operator with associated multiplierσ satisfying certain Sobolev regularity.

关键词： bilinear Fourier multiplier Morrey space weighted norm inequality

Criterion　on　weighted　L~p－Boundedness　for　Oscillatory　Singular　Integrals　with　Rough　Kernel

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新疆大学学报(自然科学版)(中英文) 1995年第3期 14-14页

作者： Jiang Yinsheng(Department of Mathematics of Xinjiang University,China)

ＣｒｉｔｅｒｉｏｎｏｎＷｅｉｇｈｔｅｄＬ~ｐ－ＢｏｕｎｄｅｄｎｅｓｓｆｏｒＯｓｃｉｌｌａｔｏｒｙＳｉｎｇｕｌａｒＩｎｔｅｇｒａｌｓｗｉｔｈＲｏｕｇｈＫｅｒｎｅｌ￥ＪｉａｎｇＹｉｎｓｈｅｎｇ(ＤｅｐａｒｔｍｅｎｔｏｆＭａ... 详细信息

ＣｒｉｔｅｒｉｏｎｏｎＷｅｉｇｈｔｅｄＬ~ｐ－ＢｏｕｎｄｅｄｎｅｓｓｆｏｒＯｓｃｉｌｌａｔｏｒｙＳｉｎｇｕｌａｒＩｎｔｅｇｒａｌｓｗｉｔｈＲｏｕｇｈＫｅｒｎｅｌ￥ＪｉａｎｇＹｉｎｓｈｅｎｇ(ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓｏｆＸｉｎｊｉ?..

关键词： weighted norm inequality oscillatory singular integral block space