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具有非倍测度的Littlewood-Paley gλ^＊函数的多线性交换子的端点估计
  • ISSN号：0583-1431
  • 期刊名称：《数学学报》
  • 时间：0
  • 分类：O174.1[理学—数学;理学—基础数学]
  • 作者机构：[1]北京师范大学数学科学学院数学与复杂系统教育部重点实验室,北京100875, [2]罗湖区罗湖外语学校初中部,深圳市518004
  • 相关基金：国家自然科学基金重点资助项目（10931001）; 国家自然科学基金青年基金资助项目（10701010）; 北京市自然科学基金资助项目（1102023）; 长江学者和创新团队发展计划资助
作者： 薛庆营[1], 张钜玚[2], 李文娟[1]
关键词： gλ^＊函数, LITTLEWOOD-PALEY算子, 多线性交换子, g_λ^＊ function, Littlewood-Paley operator, multilinear commutators
中文摘要：

令μ是R~d上可能为非倍的正的Radon测度.对于所有的x∈R~d,r〉0以及某个固定的常数C_0,μ只需满足μ（B（x,r））≤C_0r~n（0〈n≤d）.本文定义了带有非倍测度的Littlewood-Paley函数的多线性交换子g_（λ,μ,b,m）~＊（f）（x）=g_（λ,μ）~＊（[b（x）-b（·）]~mf）（x）,其中x∈R~d,并主要研究了它在非倍测度下的端点估计.这些估计可以认为是相关经典结果的更一般化推广.

英文摘要：

Letμbe a positive Radon measureμon R~d which may be non-doubling.The only condition thatμisμ（B（x,2r））≤C_0μ（B（x,r））for all x∈R~d,r0 and somefixed constant C_0.In this paper,the authors define Littlewood-Paley＇s g_（λ,b,m）~＊ functionas follows：g_（λ,b,m）~＊（x）=g_λ~＊（[b（x）—b（·）]~mf）（x）,x∈R~d,and mainly studied its endpointestimates when they are related to non-doubling measureμ.These estimates can beconsidered as extensions of related classical results.

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期刊信息
  • 《数学学报》
  • 北大核心期刊（2011版）
  • 主管单位:中国科学院
  • 主办单位:中国科学院数学与系统科学研究院数学研究院
  • 主编：李炳仁
  • 地址：北京市海淀区中关村东路55号
  • 邮编：100080
  • 邮箱：Actamath@amss.ac.cn
  • 电话：010-62551910
  • 国际标准刊号：ISSN：0583-1431
  • 国内统一刊号：ISSN：11-2038/O1
  • 邮发代号:2-502
  • 获奖情况:
  • 1996年中科院优秀科技期刊二等奖,1997年全国优秀科技期刊二等奖,2000年中科院优秀科技期刊二等奖
  • 国内外数据库收录:
  • 美国数学评论（网络版）,德国数学文摘,荷兰文摘与引文数据库,日本日本科学技术振兴机构数据库,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,中国北大核心期刊（2000版）
  • 被引量:9981