多线性Marcinkiewicz积分交换子的加权端点估计

数学物理学报 ›› 2012, Vol. 32 ›› Issue (5): 892-903.

多线性Marcinkiewicz积分交换子的加权端点估计

张璞¹|武江龙¹|刘庆国²

1.牡丹江师范学院数学系黑龙江牡丹江 157011|2.Laboratory for Multiphase Processes, University of Nova Gorica, Nova Gorica 5000, |Slovenia

收稿日期:2010-10-08 修回日期:2012-04-06 出版日期:2012-10-25 发布日期:2012-10-25
基金资助:
黑龙江省自然科学基金(A200913)资助

Weighted Endpoint Estimates for Multilinear Commutators of Marcinkiewicz Integrals

ZHANG Pu¹, WU Jiang-Long¹, LIU Qiang-Guo²

1.Department of Mathematics, Mudanjiang Normal University, Heilongjiang Mudanjiang 157011|2.Laboratory for Multiphase Processes, University of Nova Gorica, Nova Gorica 5000, Slovenia

Received:2010-10-08 Revised:2012-04-06 Online:2012-10-25 Published:2012-10-25
Supported by:
黑龙江省自然科学基金(A200913)资助

摘要/Abstract

摘要：

μ_Ω,b是由n 维Marcinkiewicz积分μ_Ω和b_j∈BMO(Rⁿ)(1≤j ≤m)生成的多线性交换子, 当Ω满足一类Dini型条件时, 建立了μ_Ω,b的加权弱L(log L)^m -型估计.

关键词: Marcinkiewicz 积分, 多线性交换子, BMO(Rⁿ), A_p 权

Abstract:

Let μ_Ω,b be the multilinear commutator generalized by μ_Ω, the n-dimensional Marcinkiewicz integral, and b_j∈BMO(Rⁿ)(1≤j ≤m). The authors establish the weighted weak L(log L)^m -type estimates for μ_Ω,b when Ω satisfies a kind of Dini conditions.

Key words: Marcinkiewicz integral, Multilinear commutator, BMO(Rⁿ), A_p weight

中图分类号:

42B20

张璞, 武江龙, 刘庆国. 多线性Marcinkiewicz积分交换子的加权端点估计[J]. 数学物理学报, 2012, 32(5): 892-903.

ZHANG Pu, WU Jiang-Long, LIU Qiang-Guo. Weighted Endpoint Estimates for Multilinear Commutators of Marcinkiewicz Integrals[J]. Acta mathematica scientia,Series A, 2012, 32(5): 892-903.

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