郭燕,孟岩.某些算子和交换子在非齐型空间上的Morrey-Herz空间中的有界性[J].数学研究及应用,2008,28(2):371~382
某些算子和交换子在非齐型空间上的Morrey-Herz空间中的有界性
Boundedness of Some Operators and Commutators in Morrey--Herz Spaces on Non-Homogeneous Spaces
投稿时间:2006-01-09  修订日期:2006-07-06
DOI:10.3770/j.issn:1000-341X.2008.02.018
中文关键词:  Hardy-Littlewood极大算子  Calder\'on-Zygmund算子  分数次积分算子  RBMO$(\mu)$函数  多线性交换子  齐次Morrey-Herz空间  弱齐次Morrey-Herz空间  非齐型空间.
英文关键词:Hardy-Littlewood maximal operators  Calder\'on-Zygmund operators  fractional integral operators  RBMO$(\mu)$ functions  multilinear commutators  homogeneous Morrey-Herz spaces  weak homogeneous Morrey-Herz spaces  non-homogeneous spaces.
基金项目:华北电力大学青年基金(No.200611004); 中国人民大学科学基金(No.30206104).
作者单位
郭燕 华北电力大学数理系, 河北 保定 071003 
孟岩 中国人民大学信息学院, 北京 100872 
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中文摘要:
      引入了非齐型空间上的齐次Morrey-Herz 空间和弱齐次Morrey-Herz空间并建立了Hardy-Littlewood极大算子,Calder\'on-Zygmund算子和分数次积分算子在齐次Morrey-Herz空间中的有界性以及在弱齐次Morrey-Herz空间中的弱型估计. 此外,还证明了$\rb$函数与Calder\'on-Zygmund算子或分数次积分算子生成的多线性交换子以及与Hardy-Littlewood极大算子相关的极大交换子在齐次Morrey-Herz空间中的有界性.
英文摘要:
      The authors introduce the homogeneous Morrey-Herz spaces and the weak homogeneous Morrey-Herz spaces on non-homogeneous spaces and establish the boundedness in homogeneous Morrey-Herz spaces for a class of sublinear operators including Hardy-Littlewood maximal operators, Calder\'on-Zygmund operators and fractional integral operators. Furthermore, some weak estimate of these operators in weak homogeneous Morrey-Herz spaces are also obtained. Moreover, the authors discuss the boundedness in homogeneous Morrey-Herz spaces of the maximal commutators associated with Hardy-Littlewood maximal operators and multilinear commutators generated by Calder\'on-Zygmund operators or fractional integral operators with RBMO$(\mu)$ functions.
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