极大高阶交换子的端点估计

数学物理学报 ›› 2012, Vol. 32 ›› Issue (2): 320-335.

极大高阶交换子的端点估计

乔丹|杨美金|陈建仁

哈尔滨师范大学数学科学学院哈尔滨 150025

收稿日期:2010-09-22 修回日期:2011-11-18 出版日期:2012-04-25 发布日期:2012-04-25
基金资助:
国家自然科学基金(11071052)和哈尔滨师范大学博士项目资助

Endpoint Estimates for Higher Order Maximal Commutators

QIAO Dan, YANG Mei-Jin, CHEN Jian-Ren

School of Mathematical Sciences, Harbin Normal University, Harbin 150025

Received:2010-09-22 Revised:2011-11-18 Online:2012-04-25 Published:2012-04-25
Supported by:
国家自然科学基金(11071052)和哈尔滨师范大学博士项目资助

摘要/Abstract

摘要：

该文主要确立了当b∈BMO 时, 极大高阶奇异积分算子交换子T_{b, m}* 满足如下不等式

|{y∈Rⁿ:T_{b, m}*f(y)>λ}|≤C||b||^m_BMO∫_Rⁿ|f(y)|/λ (1+log⁺|f(y)|/λ)^mdy
且T_{b, m}* 在L^p(Rⁿ)(1 < p <∞上有界.

关键词: 极大高阶交换子, 奇异积分算子, 双倍Young 函数

Abstract:

In this paper, the authors establish that higher order maximal commutators of singular integral operator T_{b, m}* satisfy the following inequality
|{y∈Rⁿ:T_{b, m}*f(y)>λ}|≤C||b||^m_BMO∫_Rⁿ|f(y)|/λ (1+log⁺|f(y)|/λ)^mdy
and are bounded on L^p(Rⁿ), 1 < p <∞, when b is a
BMO function.

Key words: Higher order maximal commutators, Singular integral operator, Doubling Young function

中图分类号:

42B20

乔丹, 杨美金, 陈建仁. 极大高阶交换子的端点估计[J]. 数学物理学报, 2012, 32(2): 320-335.

QIAO Dan, YANG Mei-Jin, CHEN Jian-Ren. Endpoint Estimates for Higher Order Maximal Commutators[J]. Acta mathematica scientia,Series A, 2012, 32(2): 320-335.

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