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BOUNDEDNESS OF THE CALDER´ON COMMUTATOR WITH A ROUGH KERNEL ON TRIEBEL-LIZORKIN SPACES

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Acta Mathematica Scientia 2023年第4期43卷 1618-1632页

作者：胡国恩刘洁 Center of Fundamental Science Huanghe Science and Technology UniversityZhengzhou 450063China

In this paper,we consider the boundedness on Triebel-Lizorkin spaces for the d-dimensional Calder´on commutator defined by TΩ,af(x)=p.v.∫R_(d)Ω(x−y)/|x−y|^(d+1)(a(x)−a(y))f(y)dy,where Ω is homogeneous of degree zero,integrable on Sd−1 and has a vanishing moment of order one,and a is a function on Rd such that∇a∈L^(∞)(R^(d)).We prove that if 1

关键词： Calder´on commutator Fourier transform Littlewood-Paley theory Calder´on reproducing formula

Estimates for multUinear singular integral operators with nonsmooth kernels

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Frontiers of Mathematics in China 2012年第1期7卷 51-67页

作者： guoen hu Yan MENG Department of Applied Mathematics Zhengzhou Information Science and TechnologyInstitute Zhengzhou 450002 China School of Information Renmin University of China Beijing 100872 China

Let （H,d,μ） be a space of homogeneous type in the sense of Coifman and Weiss. In this paper, we consider the behavior on Lp^p1 （X） x ... x LP^m（X） for the m-linear singular integral operators with nonsmooth ker... 详细信息

关键词： Approximation to the identity multilinear singular integraloperator nonsmooth kernel

Compactness of the commutators of homogeneous singular integral operators

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Science China Mathematics 2015年第11期58卷 2347-2362页

作者： GUO XiaoLi hu guoen College of Mathematics and Information Science Zhengzhou University of Light Industry Department of Applied Mathematics Zhengzhou Information Science and Technology Institute

Let TΩ be the singular integral operator with kernel Ω(x)/|x|~n,where Ω is homogeneous of degree zero,integrable and has mean value zero on the unit sphere S^(n-1).In this paper,by Fourier transform estimates,Littlewood-Paley theory and approximation,the authors prove that if Ω∈L(lnL)~2(S^(n-1)),then the commutator generated by T_Ω and CMO(R^n) function,and the corresponding discrete maximal operator,are compact on L^p(R^n,|x|^(γp)) for p∈(1,∞) and γ_p ∈(-1,p-1).

关键词：奇异积分算子均匀度交换子紧性傅里叶变换 Sn-1 单位球面极大算子

ON A MULTILINEAR OSCILLATORY SINGULAR INTEGRAL OPERATOR (I)

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Chinese Annals of Mathematics,Series B 1997年第2期18卷 181-190页

作者： CHEN WENGU hu guoen LU SHANZHEN Department of Mathematics Beijing Normal UniversityBeijing 100875China.

The authors consider the multilinear oscillatory singular integral operator defined by T A 1,A 2,…,A k f(x)=∫ R n e iP(x,y) ∏k j=1 R m j (A j;x,y)Ω(x-y)|x-y| n+M f(y)dy,where ... 详细信息

The authors consider the multilinear oscillatory singular integral operator defined by T A 1,A 2,…,A k f(x)=∫ R n e iP(x,y) ∏k j=1 R m j (A j;x,y)Ω(x-y)|x-y| n+M f(y)dy,where P(x,y) is a real-valued polynomial on R n× R n , Ω is homogeneous of degree zero, R m j (A j;x,y) denotes the m j -th order Taylor series remainder of A j at x expanded about y , M=∑kj=1 m j . It is shown that if Ω belongs to the space L log +L(S n-1 ) and has vanishing moment up to order M , then‖T A 1,A 2,…,A k f‖ q C ∏kj=1∑|α|=mj‖D αA j‖ r j ‖f‖ p, provided that 1

关键词： Multilinear operator Oscillatory singularintegral Maximal operator

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

ON A MULTILINEAR SINGULAR INTEGRAL OPERATOR

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Analysis in Theory and Applications 1995年第4期11卷 90-107页

作者： hu guoen(Beijing Normal University, China) Department of Mathematics Beijing Normal University Beijing PRC

In this paper, we prove that the maximal operatorsatisfiesis homogeneous of degree 0, has vanishing moment up to order M and satisfies Lq-Dini condition for some

关键词： show ON A MULTILINEAR SINGULAR INTEGRAL OPERATOR Math II BMO

AN ENDPOINT ESTIMATE FOR THE COMMUTATORS OF SINGULAR INTEGRALS WITH NON DOUBLING MEASURES

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Analysis in Theory and Applications 2003年第1期19卷 29-36页

作者： hu guoen and Jiao Yulan (University of Information Engineering, China) Department of Applied Mathematics University of Information Engineering Zhengzhou P. R. China School of Science University of Information Engineering Zhengzhou P. R. China

A weak type endpoint estimate is established for commutators of the Calderon-Zygmund singular integrals on Rd with non doubling measures.

关键词： singular integral commutator,doubling measure

Weighted norm inequalities for the multilinear Calderón-Zygmund operators

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Science China Mathematics 2010年第7期53卷 1859-1872页

作者： hu guoen Department of Applied Mathematics, Zhengzhou Information Sciences and Technology Institute,Zhengzhou 450002, China Department of Applied Mathematics Zhengzhou Information Sciences and Technology Institute Zhengzhou China

In this paper, by proving some suitable weighted endpoint estimates, and then by multilinear interpolation and a new multilinear extrapolation lemma, the author establishes some weighted estimates for the multilinear ... 详细信息

关键词： multilinear Calderón-Zygmund operator commutator weighted norm inequality interpolation extrapolation

QUANTITATIVE WEIGHTED BOUNDS FOR A CLASS OF SINGULAR INTEGRAL OPERATORS

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Acta Mathematica Scientia 2019年第4期39卷 1149-1162页

作者：高文华胡国恩 School of Applied Mathematics Beijing Normal University

In this article, the authors consider the weighted bounds for the singular integral operator defined by TAf(x)=p.v.∫Rn Ω(x-y)/|x-y|n+1(A(x)-A(y)-▽A(y))f(y)dy,where Ω is homogeneous of degree zero and has vanishing moment of order one, and A is a function on Rn such that ▽A ∈ BMO(R^n). By sparse domination, the authors obtain some qua nt itative weighted bounds for Ta when Q satisfies regularity condition of L^τ-Dini type for some r∈(1,∞).

关键词： Singular integral operator sparse domination Ap constant maximal opera tor