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singular integral operators on New BMO and Lipschitz Spaces of Homogeneous Type

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Journal of Mathematical Research with Applications 2016年第1期36卷 97-108页

作者： Peng LI Jiang ZHOU School of Mathematics and System Sciences Xinjiang University

Let（X, d, μ） be a space of homogeneous type, BMO;（X） and Lip;（β,X） be the space of BMO type,lipschitz type associated with an approximation to the identity {A;};>0 and introduced by Duong,Yan and Tang, respectively. Assuming that T is a bounded linear operator on L;（X）, we find the sufficient condition on the kernel of T so that T is bounded from BMO（X） to BMO;（X） and from Lip（β, X） to Lip;（β, X）. As an application, the boundedness of Calderón-Zygmund operators with nonsmooth kernels on BMO（R;） and Lip（β, R;） are also obtained.

关键词： singular integral operators BMO spaces Lipschitz spaces heat kernel spaces of homogeneous type

ON THE COMMUTATORS OF singular integral operators

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Acta Mathematica Scientia 2005年第3期25卷 545-554页

作者：胡国恩 Department of Applied Mathematics University of Information Engineering

Lp(Rn) (1singular integral operators. A condition on the associated kernel is given under which the L2(Rn) boundedness of the ... 详细信息

Lp(Rn) (1singular integral operators. A condition on the associated kernel is given under which the L2(Rn) boundedness of the singular integral operators implies the LP(Rn) boundedness (1

关键词： Commutator singular integral operators BMO(R^n) interpolation

Characterizations of Bounded singular integral operators on the Fock Space and Their Berezin Transforms

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Analysis in Theory and Applications 2023年第2期39卷 105-119页

作者： Xingtang Dong Li Feng School of Mathematics Tianjin UniversityTianjin 300350China

There is a singular integral operators Sj on the Fock space F2(C),which originated from the unitarily equivalent version of the Hilbert transform on L2(R).In this paper,we give an analytic characterization of functions j with finite zeros such that the integral operator Sj is bounded on F2(C)using Hadamard’s factorization *** an application,we obtain a complete characterization for such symbol functions j such that the Berezin transform of Sj is bounded while the operator Sj is ***,the corresponding problem in higher dimensions is considered.

关键词： Fock space singular integral operators boundedness Berezin transform

AN OPERATORIAL APPROACH TO singular integral EQUATIONS OF A MODIFIED TYPE

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Acta Mathematica Scientia 2008年第4期28卷 763-769页

作者：贺福利杜金元 School of Mathematics and Statistics Wuhan University Department of Mathematics Hubei Institute for Nationalities

In this article,the authors discuss a kind of modified singular integral equations on a disjoint union of closed contours or a disjoint union of open *** authors introduce some singular integral operators associated with this kind of singular integral equations,and obtain some useful properties for *** operatorial approach is also given together with some illustrated examples.

关键词： singular integral equations singular integral operators operatorial approach

MIXED HARDY SPACES AND THEIR APPLICATIONS

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Acta Mathematica Scientia 2020年第4期40卷 945-969页

作者： Wei DING Yueping ZHU School of Sciences Nantong UniversityNantong 226007China Department of Mathematics Nantong Normal CollegeNantong 226010China

Multi-parameter mixed Hardy space Hpmix is introduced by a new discrete Calderon's *** an application,we obtain the Hmix^p→ L^p(R^n1+n2)boundedness of operators in the mixed Journe’s class.

关键词： mixed Hardy spaces discrete Calderon's identity singular integral operators atoms

A CLASS OF NONLINEAR BOUNDARY VALUE PROBLEMS FOR THE SECOND-ORDER E_2 CLASS ELLIPTIC SYSTEMS IN GENERAL FORM

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Applied Mathematics and Mechanics(English Edition) 2003年第2期24卷 163-181页

作者：李明忠徐定华 DepartmentofMathematics

A class of nonlinear boundary value problems(BVP) for the second_order E 2 class elliptic systems in general form is discussed. By introducing a kind of transformation,this kind of BVP is reduced to a class of generalized nonlinear Riemann_Hilbert BVP. And then some singular integral operators are introduced to establish the equivalent nonlinear singular integral equations. The solvability is proved under some suitable hypotheses by means of the properties of singular integral operators and the function theoretic methods.

关键词： elliptic systems boundary value problems singular integral equations singular integral operators existence

Estimates of Some integral operators with Bounded Variable Kernels on the Hardy and Weak Hardy Spaces over R^n

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Acta Mathematica Sinica,English Series 2016年第4期32卷 411-438页

作者： Hua WANG College of Mathematics and Econometrics Hu'nan University

In this paper,we first introduce Lσ1-（log L）σ2 conditions satisfied by the variable kernelsΩ（x,z） for 0≤σ1≤1 and σ2≥*** these new smoothness conditions,we will prove the boundedness properties of singular integral operators TΩ,fractional integrals TΩ,α and parametric Marcinkiewicz integrals μΩρ with variable kernels on the Hardy spaces Hp（Rn） and weak Hardy spaces WHP（Rn）.Moreover,by using the interpolation arguments,we can get some corresponding results for the above integral operators with variable kernels on Hardy-Lorentz spaces Hp,q（Rn） for all p 〈 q 〈 ∞.

关键词： singular integral operators fractional integrals parametric Marcinkiewicz integrals variable kernels Hardy spaces H^p(R^n) weak Hardy spaces WH^p(R^n) Hardy-Lorentz spaces Hp,q(Rn)

MIXED LIPSCHITZ SPACES AND THEIR APPLICATIONS

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Acta Mathematica Scientia 2022年第2期42卷 690-714页

作者： Shaoyong HE Jiecheng CHEN Department of Mathematics Huzhou UniversityHuzhou 313000China Department of Mathematics Zhejiang Normal UniversityJinhua 321004China

The purpose of this paper is to introduce bi-parameter mixed Lipschitz spaces and characterize them via the Littlewood-Paley *** an application,we derive a boundedness criterion for singular integral operators in a mixed Journéclass on mixed Lipschitz *** elements of the paper are the development of the Littlewood-Paley theory for a special mixed Besov spaces,and a density argument for the mixed Lipschitz spaces in the weak sense.

关键词： Mixed Lipschitz spaces Littlewood-Paley theory singular integral operators

singular integrals on Product Spaces with Mixed Norms

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Chinese Quarterly Journal of Mathematics 2022年第2期37卷 214-220页

作者： WANG Xiao School of Mathematical Sciences Nankai UniversityTianjin 300071China

In this paper,we prove the boundedness of the singular integral operators on product spaces with mixed norms and obtain the endpoint weak-type estimates.

关键词： singular integral operators Mixed norms Product spaces