WEIGHTED ESTIMATES WITH GENERAL WEIGHTS FOR MULTILINEAR CALDER´|ON-ZYGMUND OPERATORS

doi:10.1016/S0252-9602(12)60121-0

数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (4): 1529-1544.doi: 10.1016/S0252-9602(12)60121-0

WEIGHTED ESTIMATES WITH GENERAL WEIGHTS FOR MULTILINEAR CALDER´|ON-ZYGMUND OPERATORS

胡国恩

Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou 450002, China

收稿日期:2010-08-02 修回日期:2011-04-15 出版日期:2012-07-20 发布日期:2012-07-20
基金资助:
The research was supported by the NSFC (10971228).

WEIGHTED ESTIMATES WITH GENERAL WEIGHTS FOR MULTILINEAR CALDER´|ON-ZYGMUND OPERATORS

HU Guo-En

Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou 450002, China

Received:2010-08-02 Revised:2011-04-15 Online:2012-07-20 Published:2012-07-20
Supported by:
The research was supported by the NSFC (10971228).

摘要/Abstract

摘要：

In this paper, some weighted estimates with general weights are established for the m-linear Calder´on-Zygmund operator and the corresponding maximal operator. It is proved that, if p₁, · · · , p_m ∈ [1,∞] and p ∈ (0,∞) with 1/p =∑^m_k₌₁1/p_k, then for any weight w, integer l with 1 ≤ l ≤ m, these operators are bounded from L^p¹ (Rⁿ, M_Bw) ×· · ·×L^pl(Rⁿ, M_Bw)×L^pl⁺¹ (Rⁿ, Mw)×· · ·×L^pm(Rⁿ, Mw) to L^p^,∞(Rⁿ, w) or Lp(Rn,w), where B is a Young function and MB is the maximal operator associated with B.

关键词: multilinear Calder´on-Zygmund operator, maximal operator, weighted norm inequality, Calder´on-Zygmund decomposition

Abstract:

Key words: multilinear Calder´on-Zygmund operator, maximal operator, weighted norm inequality, Calder´on-Zygmund decomposition

中图分类号:

42B20

胡国恩. WEIGHTED ESTIMATES WITH GENERAL WEIGHTS FOR MULTILINEAR CALDER´|ON-ZYGMUND OPERATORS[J]. 数学物理学报(英文版), 2012, 32(4): 1529-1544.

HU Guo-En. WEIGHTED ESTIMATES WITH GENERAL WEIGHTS FOR MULTILINEAR CALDER´|ON-ZYGMUND OPERATORS[J]. Acta mathematica scientia,Series B, 2012, 32(4): 1529-1544.

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WEIGHTED ESTIMATES WITH GENERAL WEIGHTS FOR MULTILINEAR CALDER´|ON-ZYGMUND OPERATORS

WEIGHTED ESTIMATES WITH GENERAL WEIGHTS FOR MULTILINEAR CALDER´|ON-ZYGMUND OPERATORS

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