非双倍测度下的Littlewood-Paley算子的有界性

J4 ›› 2013, Vol. 48 ›› Issue (10): 78-81.

非双倍测度下的Littlewood-Paley算子的有界性

耿素丽,赵凯*,张立平

青岛大学数学科学学院,山东青岛 266071

收稿日期:2013-01-08 发布日期:2013-10-14
通讯作者: 赵凯(1960- ),男,博士,教授,研究方向为调和分析与小波分析. Email: zkzc@yahoo.com.cn
作者简介:耿素丽(1986- ),女,硕士研究生,研究方向为调和分析与小波分析. Email: linyigengsuli@163.com
基金资助:
国家自然科学基金资助项目(11041004);山东省自然科学基金资助项目(ZR2010AM032)

Boundedness of Littlewood-Paley operators with non-doubling measures

GENG Su-li, ZHAO Kai*, ZHANG Li-ping

College of Mathematics, Qingdao University, Qingdao 266071, Shandong, China

Received:2013-01-08 Published:2013-10-14

摘要/Abstract

摘要：

设μ是一个Rd上的Radon测度, 仅满足增长条件: μ(B(x,r))≤C0rn,00。假设Littlewood-Paley g函数在L2(μ)上有界, 利用非双倍测度下的Calderón-Zygmund分解证明了LittlewoodPaley g函数是 L1(μ)到L1,∞(μ)上有界的, 并且它是H1(μ)到L1(μ)上有界的。

关键词: 非双倍测度;Littlewood-Paley算子;Calderón-Zygmund分解;有界性

Abstract:

Let μ be a positive Radon measure on Rd which may be non-doubling. The only condition that μ must satisfy is μ(B(x,r))≤C0rn, for x∈Rd,r>0 and some fixed constants C0>0 and 0

Key words: non-doubling measure; Littlewood-Paley operator; Calderón-Zygmund decompsition; boundedness

中图分类号:

O174.2

耿素丽,赵凯*,张立平. 非双倍测度下的Littlewood-Paley算子的有界性[J]. J4, 2013, 48(10): 78-81.

GENG Su-li, ZHAO Kai*, ZHANG Li-ping. Boundedness of Littlewood-Paley operators with non-doubling measures[J]. J4, 2013, 48(10): 78-81.

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