向量值多线性算子的加权Lipschitz估计

数学物理学报 ›› 2011, Vol. 31 ›› Issue (4): 930-945.

向量值多线性算子的加权Lipschitz估计

周肖沙, 刘岚喆

长沙理工大学数学系长沙 410077

收稿日期:2009-05-20 修回日期:2010-07-09 出版日期:2011-08-25 发布日期:2011-08-25
基金资助:
湖南省教育厅项目(09C057)资助

Weighted Lipschitz Estimates for Vector-valued Multilinear Operators

ZHOU Xiao-Sha, LIU Lan-Zhe

Department of Mathematics, Changsha University of Science and Technology, Changsha 410077

Received:2009-05-20 Revised:2010-07-09 Online:2011-08-25 Published:2011-08-25
Supported by:
湖南省教育厅项目(09C057)资助

摘要/Abstract

摘要：

该文对由一类积分算子和加权 Lipschitz函数生成的向量值多线性算子证明了其加权有界性. 该积分算子包括 Calder\'on-Zygmund 奇异积分算子, 分数次积分算子, Littlewood-Paley 算子, Marcinkiewicz 算子和Bochner-Riesz算子.

关键词: 向量值多线性算子, Calderon-Zygmund 奇异积分算子, 分数次积分算子, Littlewood-Paley 算子, Marcinkiewicz 算子, Bochner-Riesz算子,
加权Lipschitz空间, Triebel-Lizorkin 空间

Abstract:

In this paper, the weighted boundedness for the vector-valued multilinear operators generated by some integral operators and the weighted Lipschitz functions are obtained. The operators include Calder\'on-Zygmund singular integral operator, fractional integral operator, Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator.

Key words: Vector-valued multilinear operators, Calderon-Zygmund singular integral operator, Fractional integral operator, Littlewood-Paley operator, Marcinkiewicz operator, Bochner-Riesz operator, Lipschitz space, Triebel-Lizorkin space

中图分类号:

42B20

周肖沙, 刘岚喆. 向量值多线性算子的加权Lipschitz估计[J]. 数学物理学报, 2011, 31(4): 930-945.

ZHOU Xiao-Sha, LIU Lan-Zhe. Weighted Lipschitz Estimates for Vector-valued Multilinear Operators[J]. Acta mathematica scientia,Series A, 2011, 31(4): 930-945.

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