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Weighted Estimates for Iterated Commutators of Multilinear Fractional Operators

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Acta Mathematica Sinica,English Series 2012年第9期28卷 1769-1778页

作者： Zeng Yan SI shan zhen lu School of Mathematics and Information Science He'nan Polytechnic University School of Mathematical Science Beijing Normal University

The author establishes weighted strong type estimates for iterated commutators of multi- linear fractional operators.

关键词： Multilinear fractional operators commutators weighted norm inequalities

Generalized Commutators for Marcinkiewicz Type Integrals with Variable Kernels

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Acta Mathematicae Applicatae Sinica 2011年第3期27卷 471-480页

作者： Hui-xia Mo shan-zhen lu School of Science Beijing University of Post and Telecommunications Beijing 100876 China School of Mathematical Sciences Beijing Normal University Beijing 100875 China

Let A be a function with derivatives of order m and D γ A ∈■β （0 〈 β 〈 1, ｜γ｜ = m）. The authors in the paper prove that if Ω（x, z） ∈ L ∞ （R n ） × L s （S n 1 ）（s ≥ n/（n β）） is homogenous of... 详细信息

Let A be a function with derivatives of order m and D γ A ∈■β （0 〈 β 〈 1, ｜γ｜ = m）. The authors in the paper prove that if Ω（x, z） ∈ L ∞ （R n ） × L s （S n 1 ）（s ≥ n/（n β）） is homogenous of degree zero and satisfies the mean value zero condition about the variable z, then both the generalized commutator for Marcinkiewicz type integral μ A Ω and its variation μ A Ω are bounded from L p （R n ） to L q （R n ）, where 1 〈 p 〈 n/β and 1/q = 1/p β/n. The authors also consider the boundedness of μ A Ω and its variation μ A Ω on Hardy spaces.

关键词： Marcinkiewicz integral variable kernel Lipschitz space Hardy space

Boundedness of Some Marcinkiewicz Integral Operators Related to Higher Order Commutators on Hardy Spaces

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Acta Mathematica Sinica,English Series 2006年第1期22卷 105-114页

作者： shan zhen lu Li Fang XU Department of Mathematics Beijing Normal University Beijing 100875 P. R. China

In this paper, the authors study the boundedness properties of μΩ↑m,b generated by the function b ∈Lipβ（R^n）（0 〈β≤ 1/m） and the Marcinkiewicz integrals operator μΩ. The boundednesses are established on t... 详细信息

关键词： Marcinkiewicz integral Higher order commutator Lipshcitz space Hardy type space Herz space

Commutators Generated by Multilinear Calderon-Zygmund Type Singular Integral and Lipschitz Functions

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Acta Mathematicae Applicatae Sinica 2014年第4期30卷 903-912页

作者： Hui-xia MO shan-zhen lu School of Science Beijing University of Posts and Telecommunications School of Mathematical Sciences Beijing Normal University

In this paper, we establish the boundedness of commutators generated by the multilinear Calderon- Zygmud type singular integrals and Lipschitz functions on the Triebel-Lizorkin space and Lipschitz spaces.

关键词： multilinear Calderon-Zygmud type singular integral commutator Triebel-Lizorkin space Lips-chitz space

Continuity for Maximal Multilinear Bochner-Riesz Operators on Hardy and Herz Hardy Spaces

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Acta Mathematica Sinica,English Series 2006年第1期22卷 69-76页

作者： Lan Zhe LIU shan zhen lu Department of Mathematics Changsha University of Science and Technology Changsha 410077 P. R. China Department of Mathematics Beijing Normal University Beijing 100875 P. R. China

Let Baδ^A. be the maxiamal multilinear Bochner-Riesz operators generated by Bochner Riesz operators and D^αA∈ Lipβ（｜α｜= m）, The continuity of the operator on some Hardy and Herz type Hardy is obtained.

关键词： Bochner-Riesz operator Multilinear Operators Hardy Space Herz Space Lipschitz space

Strongly Singular Integral Operators on Weighted Hardy Space

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Acta Mathematica Sinica,English Series 2006年第3期22卷 767-772页

作者： Jun Feng LI shan zhen lu Department of Mathematics Beijing Normal University

In this paper, we obtain that a strongly singular integral operator is bounded on Lω^p. space for 1 〈 p 〈 ∞. We also obtain that a strongly singular integral operator is a bounded operator from Hω^p, to Lω^p for some weight w and 0 〈 p ≤ 1. And by an atomic decomposition, we obtain that a strongly singular integral operator is a bounded operator on Hω^p for some w and 0 〈 p ≤ 1.

关键词： Strongly singular Calderón-Zygmund operators Hardy spaces A weight

L^p Boundedness for Parabolic Littlewood-Paley Operators with Rough Kernels Belonging to Block Spaces

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Acta Mathematica Sinica,English Series 2010年第2期26卷 277-286页

作者： Dong Xiang CHEN shan zhen lu School of Mathematics Beijing Normal University Beijing 100875 P. R. China and Department of Mathematics Jiangxi Normal University Nanchang 330022 P. R. China School of Mathematics Beijing Normal University Beijing 100875 P. R. China

This paper is primarily concerned with the proof of the Lp boundedness of parabolic Littlewood-Paley operators with kernels belonging to certain block spaces. Some known results are essentially extended and improved.

关键词： parabolic Littlewood-Paley operator Fourier transform rough kernel block space

Remarks on g-functions on H^n

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Acta Mathematica Sinica,English Series 2007年第1期23卷 7-16页

作者： Ming Ju LIU shan zhen lu LMIB and Department of Mathematics Beihang University Beijing 100083 P. R. China Department of Mathematics Beijing Normal University Beijing 100875 P. R. China

In this paper, the authors study some properties of Littlewood-Paley g-functions gψ（f）,lusin area functions Sψ,α（f） and Littlewood-Paley gψ^＊,λ（f） functions defined on H^n, where α,λ 〉 0 and ψ, f are s... 详细信息

关键词： Square integrable function Weight Herz spaces

Two Operators Related to Marcinkiewicz Integrals

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Acta Mathematica Sinica,English Series 2009年第10期25卷 1617-1634页

作者： Hui Xia MO shan zhen lu School of Science Beijing University of Post and Telecommunications Beijing 100876 China School of Mathematical Sciences Normal University Beijing 100875 China

In this paper, the authors consider the boundedness of generalized higher commutator of Marcinkiewicz integral μΩ^b, multilinear Marcinkiewicz integral μΩ^A and its variation μΩ^A on Herz-type Hardy spaces, here Ω is homogeneous of degree zero and satisfies a class of L^s-Dini condition. And as a special case, they also get the boundedness of commutators of Marcinkiewicz integrals on Herz-type Hardy spaces.

关键词： generalized higher commutator of Marcinkiewicz integral multilinear Marcinkiewicz integral Herz-type Hardy space Lipschitz space