Banach空间值的变指标Lebesgue空间上的Calderón-Zygmund算子（英文）  

Calderón-Zygmund Operators on Banach Space Valued Lebesgue Spaces With Variable Exponent

作　　者：沈聪辉[1] 徐景实[1] 

机构地区：[1]海南师范大学数学与统计学院,海口海南571158

出　　处：《数学进展》2017年第3期441-452,共12页Advances in Mathematics（China）

基　　金：supported by NSFC(No.11361020);the Natural Science Foundation of Hainan Province(No.20151010)

摘　　要：本文证明了带有满足H?rmander条件的算子核的向量值的Calderón-Zygmund算子在齐型的度量测度空间上的指标为全局log-H?lder连续的变指标Lebesgue空间上的有界性.作为应用,得到了向量值的Hardy-Littlewood极大算子在齐型的度量测度空间上的指标为全局log-H?lder连续的变指标Lebesgue空间上的有界性.In this paper,the authors prove that a vector-valued Calderón-Zygmund operator with an operator-valued kernel satisfying H？rmander＇s conditions is bounded on Banach space valued Lebesgue spaces with global log-H？lder continuous variable exponent over metric measure spaces of homogeneous type.As an application,the authors obtain the boundedness of the vector Hardy-Littlewood maximal operator on Lebesgue spaces with global log-H？lder continuous variable exponent over metric measure spaces of homogeneous type.

关 键 词：CALDERÓN-ZYGMUND算子 变指标 LEBESGUE空间 向量值 度量测度空间 

分 类 号：O177.2[理学—数学]