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Boundedness of Marcinkiewicz integral on Triebel-Lizorkin spaces

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Applied Mathematics(A Journal of Chinese Universities) 2010年第1期25卷 48-54页

作者： ZHANG Chun-jie chen jie-cheng College of Science Hanzhou Dianzi University Hangzhou 310018 China Department of Mathematics Zhejiang University Hangzhou 310027 China

In this paper, we prove the Triebel-Lizorkin boundedness for the Marcinkiewicz integral with rough kernel. The method we apply here enables us to consider more general operators.

关键词： Marcinkiewicz integral Triebel-Lizorkin spaces rough kernel singular integral.

L^p estimates for Riesz transform and their commutators associated with Schr?dinger type operator

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Applied Mathematics(A Journal of Chinese Universities) 2016年第1期31卷 112-126页

作者： chen Xiao-li chen jie-cheng Department of Mathematics Jiangxi Normal University Nanchang 330022 China Department of Mathematics Zhejiang Normal University Jinhua 321004 China

. Let H2 = （-△）2 ＋ V2 be the Schr6dinger type operator, where V satisfies reverse HSlder inequality. In this paper, we establish the Lp boundedness for V2 H2- 1, H21 V2, VH2- 1/2 and Hfl/2V, and that of their comm... 详细信息

关键词： Schrodinger type operator Bq class BMOL commutator.

Compactness for the commutators of multilinear singular integral operators with non-smooth kernels

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Applied Mathematics(A Journal of Chinese Universities) 2019年第1期34卷 55-75页

作者： BU Rui chen jie-cheng Department of Mathematics Qingdao University of Science and Technology Department of Mathematics Zhejiang Normal University

In this paper, the behavior for commutators of a class of bilinear singular integral operators associated with non-smooth kernels on the product of weighted Lebesgue spaces is considered. By some new maximal functions to control the commutators of bilinear singular integral operators and CMO(Rn) functions, compactness for the commutators is proved.

关键词： singular integral operator maximal function weighted norm inequality commutator compact operator

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.

Integrability of the general product Hardy operators on the product Hardy spaces

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Applied Mathematics(A Journal of Chinese Universities) 2012年第2期27卷 225-233页

作者： ZHU Xiang-rong chen jie-cheng Department of Mathematics Zhejiang Normal UniversityJinhua 321004China

In this paper,we prove that the general product Hardy operators are bounded from the product Hardy space H1n（Rm1×···×Rmn） to L1（R（∑ni=1mi）.

关键词： product Hardy operator product Hardy space atom decomposition.

Boundedness of Hausdorff operators on some product Hardy type spaces

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Applied Mathematics(A Journal of Chinese Universities) 2012年第1期27卷 114-126页

作者： chen jie-cheng FAN Da-shan ZHANG Chun-jie Department of Mathematics Zhejiang Normal UniversityJinhua 321004China Department of Mathematics University of WisconsimMilwaukeeMilwaukeeWI 53201USA School of Science Hangzhou Dianzi UniversityHangzhou 310018China

We study Hausdorff operators on the product Besov space B0,1 1 （Rn ×Rm） and on the local product Hardy space h1 （Rn ×Rm）. We establish some boundedness criteria for Hausdorff operators on these function spaces.

关键词： Hausdorff operator atomic decomposition product Besov space product Hardy space productlocal Hardy space.

Some remarks on Wente's inequality and the Lorentz-Sobolev space

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Applied Mathematics(A Journal of Chinese Universities) 2016年第3期31卷 355-361页

作者： ZHU Xiang-rong chen jie-cheng Department of Mathematica Zhejiang Normal University

In this note we consider Wente＇s type inequality on the Lorentz-Sobolev space. If f∈L^p1,q1（Rn）,G∈L^p2,q2 （Rn） and div G ≡ 0 in the sense of distribution where 1/p1＋1/p2=1/q ＋1/q2=1,1〈p1,p2〈∞, it is known that G. f belongs to the Hardy space H1 and furthermore ‖G· f‖N1≤C‖ f‖Lp1,q1（R2）‖G‖Lp2,q2（R2）Reader can see [9] Section 4 Here we give a new proof of this result. Our proof depends on an estimate of a maximal operator on the Lorentz space which is of some independent interest. Finally, we use this inequality to get a generalisation of Bethuel＇s inequality.

关键词： Lorentz space Wente type inequality Hardy space

Boundedness of singular integrals along surfaces on Lebesgue spaces

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Applied Mathematics(A Journal of Chinese Universities) 2010年第2期25卷 192-198页

作者： ZHANG Yan-dan chen jie-cheng ZHANG Chun-jie Department of Mathematics Zhejiang University of Technology Hangzhou 310023 China Department of Mathematics Zhejiang University Hangzhou 310027 China College of Science Hangzhou Dianzi University Hangzhou 310018 China

In the paper, we establish the LP（Rn＋1）-boundedness for a class of singular integral operators associated to surfaces of revolution {（y,γ（｜y｜）, y ∈ Rn} with rough kernels. We also give several applications o... 详细信息

关键词： Singular integrals surfaces rough kernels Plancherel's theorem oscillatory singular integrals.

A∞ weight estimates for vector-valued commutators of multilinear fractional integral

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Applied Mathematics(A Journal of Chinese Universities) 2013年第3期28卷 335-357页

作者： YU Xiao chen jie-cheng ZHANG Yan-dan Department of Mathematics Zhejiang University Department of Mathematics Shangrao Normal University Department of Mathematics Zhejiang Normal University Department of Mathematics Zhejiang University of Science and Technology

In this paper, the authors get the Coifman type weighted estimates and weak weighted LlogL estimates for vector-valued generalized commutators of multilinear fractional integral with w ∈ A∞. Furthermore, both the boundedness of vector-valued multilinear frac- tional integral and the weak weighted LlogL estimates for vector-valued multilinear fractional integral are also obtained.

关键词： vector-valued commutator multilineax fractional integral weighted.