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Mk-Type Sharp Estimates and Boundedness on Morrey Space for Toeplitz Type operators Associated to Fractional integral and singular integral operator with Non-Smooth Kernel

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Journal of Mathematical Research with Applications 2021年第5期41卷 481-496页

作者： Dazhao CHEN School of Science Shaoyang University

In this paper, we prove the Mk-type sharp maximal function estimates for the Toeplitz type operators associated to the fractional integral and singular integral operator with non-smooth kernel. As an application, we o... 详细信息

关键词： Toeplitz type operator singular integral operator fractional integral operator sharp maximal function BMO Morrey space

Weighted Estimates for the Maximal Commutator of singular integral operator on Spaces of Homogeneous Type

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Communications in Mathematical Research 2010年第1期26卷 53-66页

作者： ZHANG HAO Department of Applied Mathematics Information Engineering University Zhengzhou 450002

Weighted estimates with general weights are established for the maximal operator associated with the commutator generated by singular integral operator and BMO function on spaces of homogeneous type, where the associated kernel satisfies the HSlder condition on the first variable and some condition which is fairly weaker than the Holder condition on the second variable.

关键词： spaces of homogeneous type weighted estimates singular integral operator commutator maximal operator

The Boundedness of singular integral operator along an Open Curve

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Wuhan University Journal of Natural Sciences 1998年第4期3卷 383-388页

作者： Wang Xiaolin Min Honglin(College of Mathematical Sciences, Wuhan University, Wuhan 430072, China) College of Mathematical Sciences Wuhan University Wuhan China

It is well known that, the singular integral operatorS defined as: ifL is a closed smooth contour in the complex plane C, thenS is a bounded linear operator fromH μ(L) intoH μ(L): ifL is an open smooth curve, thenS is just a linear operator fromH * intoH *. In this paper, we define a Banach space , and prove that is a bounded linear operator, then verify the boundedness of other kinds of singular integral operators.

关键词： singular integral operator space boundedness

singular integral operatorS IN L^2 SPACEWITH CHEBYSHEV WEIGHTS

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Acta Mathematica Scientia 2000年第1期20卷 63-67页

作者：龚亚方杜金元 College of Mathematical Sciences Wuhan University Wuhan 430072 China

This paper defines a class of singular integral operators (I) over tilde(wj) on L-wj(2) space, where wights w(j)(j = 1 - 4) are lour kinds of Chebyshev weights. The authors prove that (I) over tilde(wj) is an unique linear extension of classic singular integral operator I-wj on Holder space, some important properties of (I) over tilde(wj) and some results of singular integral equation in L-wj(2) space.

关键词： singular integral operator Chebyshev weight

singular integral operatorS IN L^2 SPACES ASSOCIATED WITH THE GENERALIZED JACOBI WEIGHTS

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Acta Mathematica Scientia 2002年第4期22卷 484-488页

作者：龚亚方杜金元 Department of Mathematics Wuhan University Wuhan 430072 China

In this paper, a kind of new definitions of singular integral operators in the weighted L-2 space with the generalized Jacobi weights are given, then the boundedness in the weighted L-2 space, the relationships between these operators and the classic singular integral operators are proved. For the convenience in the later use, similar results in the L-2 space with Jacobi weights are given.

关键词： singular integral operator generalized Jacobi weight index

Boundary properties for several singular integral operators in real Clifford analysis

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Applied Mathematics(A Journal of Chinese Universities) 2010年第3期25卷 349-358页

作者： YANG He-ju XIE Yong-hong College of Mathematics and Information Science Hebei Normal University Shijiazhuang 050016 China College of Science Hebei University of Science and Technology Shijiazhuang 050018 China

On the basis of the Cauchy integral formulas for regular and biregular functions, we define some Cauchy-type singular integral operators. Then we discuss the Holder continuous property of some singular integral operators with one integral variable. Then we divide a singular integral operator with two variables into three parts and prove its Holder continuous property on the boundary.

关键词： singular integral operator Holder continuous function boundary property.

Weighted estimates for commutators of singular integral operators with non-smooth kernels

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Applied Mathematics(A Journal of Chinese Universities) 2010年第3期25卷 318-324页

作者： ZHANG Lin JIANG Yin-sheng Department of Applied Mathematics Xinjiang Institue of Finance and Economics Xinjiang 830012 China. College of Mathematics and Systems Science Xinjiang University Xinjiang 830046 China

In this paper, we establish the boundedness of commutators of singular integral operators with non-smooth kernels on weighted Lipschitz spaces Lipβ,ω. The condition on the kernel in this paper is weaker than the usu... 详细信息

关键词： Lipβ,ω space commutator singular integral operator non-smooth kernel.

Weighted norm inequalities with multiple-weight for singular integral operators with non-smooth kernels

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Frontiers of Mathematics in China 2016年第1期11卷 1-19页

作者： Rui BU Houyu JIA Department of Mathematics Zhejiang University Hangzhou 310027 China

By sharp maximal function, we establish a weighted estimate with multiple-weight for the multilinear singular integral operators with non-smooth kernels.

关键词： singular integral operator multiple weight sharp maximalfunction weighted estimate approximation to identity

Characterization of Lipschitz Functions via Commutators of Multilinear singular integral operators in Variable Lebesgue Spaces

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Acta Mathematica Sinica,English Series 2023年第12期39卷 2465-2488页

作者： Jiang Long WU Pu ZHANG Department of Mathematics Mudanjiang Normal UniversityMudanjiang 157011P.R.China

Let 6=(bi,b2,...,bm)be a collection of locally integrable functions and T,the com-mutator of multilinear singular integral operator *** by L(δ)and L(δ(·))the Lipschitz spaces and the variable Lipschitz spaces,*** main purpose of this paper is to establish some new characterizations of the(variable)Lipschitz spaces in terms of the boundedness of multilinear commutator T∑b in the context of the variable exponent Lebesgue spaces,that is,the authors give the necessary and sufficient conditions for bj(j=1,2,...,m)to be L(δ)or L(δ(·))via the boundedness of multilinear commutator from products of variable exponent Lebesgue spaces to variable exponent Lebesgue *** authors do so by applying the Fourier series technique and some pointwise esti-mate for the *** key tool in obtaining such pointwise estimate is a certain generalization of the classical sharp maximal operator.

关键词： Multilinear commutator singular integral operator Lipschitz function variable exponent