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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 M~k-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 ... 详细信息

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

Boundedness of fractional integral operators on α-modulation spaces

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Applied Mathematics(A Journal of Chinese Universities) 2014年第3期29卷 339-351页

作者： WU Xiao-mei CHEN Jie-cheng Xingzhi Colledge Zhejiang Normal University Department of Mathematics Zhejiang Normal University

In this paper, we obtain the boundedness of the fractional integral operators, the bilineax fractional integral operators and the bilinear Hilbert transform on α-modulation spaces.

关键词： α-modulation space fractional integral operator bilinear fractional integral operator bilinearHilbert transform.

Modulation space estimates for the fractional integral operators

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Science China Mathematics 2011年第7期54卷 1479-1489页

作者： ZHONG Yong CHEN JieCheng Department of Mathematics Zhejiang University Hangzhou 310027 China Department of Mathematics Zhejiang Normal University Jinhua 321004 China

We obtain the boundedness for the fractional integral operators from the modulation Hardy space μp,q to the modulation Hardy space μr,q for all 0 < p < ∞. The result is an extension of the known result for the case... 详细信息

We obtain the boundedness for the fractional integral operators from the modulation Hardy space μp,q to the modulation Hardy space μr,q for all 0 fractional operators.

关键词： modulation spaces modulation Hardy spaces fractional integral operator bilinear fractional integral operator

Necessary and Sufficient Conditions for Boundedness of Commutators of Bilinear fractional integral operators on Morrey Spaces

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Journal of Mathematical Research with Applications 2016年第6期36卷 711-717页

作者： Suixin HE Jiang ZHOU School of Mathematics and System Sciences Xinjiang University

In this paper,we obtain that b∈ BMO（R） if and only if the commutator[b,I]is bounded from the Morrey spaces L（R）×L（R） to L（R）,for some appropriate indices p,q,λ,μ.Also we show that b ∈ Lip（R） if and only if the commutator[b,I]is bounded from the Morrey spaces L（R）×L（R） to L（R）,for some appropriate indices p,q,λ,μ.

关键词： fractional integral operator Morrey spaces commutators BMO Lipschitz

BOUNDEDNESS OF fractional integral operatorS IN HERZ-TYPE SPACES ON LOCALLY COMPACT VILENKIN GROUPS

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Approximation Theory and Its Applications 2002年第3期18卷 15-25页

作者： Lan Senhua (Lishui Teachers College, China) Department of Mathematics Lishui Teachers’ College Lishui Zhejiang P R China

Let G be a locally compact Vilenkin group. In this paper toe first establish the Hardy-Littlewood-Sobolev theorem on G. Then some boundedness theorems of fractional integral operators in Herz-type spaces on G are obta... 详细信息

关键词： Homogeneous Case fractional integral operator Compact Open Subgroup Boundedness Theorem Vilenkin Group

BOUNDEDNESS OF GENERALIZED fractional integral operatorS

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Approximation Theory and Its Applications 2002年第4期18卷 38-54页

作者： TangCanqin YangDachun Changde Normal University China Beijing Normal University China

The authors introduce a new kind of fractional integral operators, namely, the so called (θ,N)-type fractional integral operators, and discuss their boundedness on the Hardy spaces, the weak Hardy spaces and the Herz... 详细信息

关键词： Hardy Space fractional integral operator Weak Hardy Space Atom Characterization Nonnegative Nondecreasing Function

Weighted Weak-type Estimates for Multilinear Commutators of fractional integrals on Spaces of Homogeneous Type

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Acta Mathematica Sinica,English Series 2007年第10期23卷 1813-1826页

作者： Osvaldo GOROSITO Gladis PRADOLINI Oscar SALINAS Department of Mathematics Consejo Nacional de Investigaciones Científicas y Técnicas de la República Argentina

We obtain weighted distributional inequalities for multilinear commutators of the fractional integral on spaces of homogeneous type, The techniques developed in this work involve the behavior of some fractional maximal functions. In relation to these operators, as a main tool, we prove a weighted weak type boundedness result, which is interesting in itself.

关键词： commutators fractional integral operator multilinear operators

Sublinear operators on block-type spaces

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Science China Mathematics 2020年第6期63卷 1107-1124页

作者： Kwok-Pun Ho Department of Mathematics and Information Technology The Education University of Hong KongHong KongChina

This study establishes the boundedness of sublinear operators on block spaces built on Banach function spaces. These results are used to study the boundedness of the Marcinkiewicz integrals, singular integral operator... 详细信息

关键词： sublinear operator Marcinkiewicz integral fractional integral operator singular integral operator block space Morrey space

BOUNDEDNESS OF MULTILINEAR fractional integral COMMUTATORS

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Applied Mathematics(A Journal of Chinese Universities) 2004年第2期19卷 212-222页

作者： WangLei PanTing Dept.ofMath. ZhejiangUniv.Hangzhou310028China Univ.ofInternationalRelation Hangzhou310015China

By introducing a kind of maximal operator of fractional order associated with the mean Luxemburg norm and using the technique of Sharp function,multilinear commutators of fractional integral operator with vector symbol b=(b 1,...,b m)defined byI b αf(x)=∫ R∏mj=1(b j(x)-b j(y))1｜x-y｜ n-αf(y)dyare *** following priori estimates are *** 101Φ1t｜｛y∈Rn:｜I b αf(y)｜>t｝｜ 1q≤ c supt>01Φ1t｜｛y∈Rn:M L(logL) 1r,α(‖b‖f)(y)>t｝｜ 1q,where ‖b‖=∏ m j=1‖b j‖ Osc expL r j,Φ(t)=t(1+log+t) 1r,1r=1r 1+...+1r m, M L(logL) 1r,α is an Orlicz type maximal operator.

关键词： fractional integral operator commutator sharp function Young function Luxemburg function.

BOUNDEDNESS FOR THE COMMUTATOR OF fractional integral ON GENERALIZED MORREY SPACE IN NONHOMOGENEOUS SPACE

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Analysis in Theory and Applications 2011年第1期27卷 51-58页

作者： Guohua Liu Lisheng Shu Anhui Normal University China

In this paper, we will establish the boundedness of the commutator generated by fractional integral operator and RBMO（μ） function on generalized Morrey space in the non-homogeneous space.

关键词： fractional integral operator commutator generalized Morrey space,RBMO(μ)