θ-型C-Z算子在加权变指数Morrey空间上的有界性  

Boundedness of θ-type C-Z Operators on Weighted Variable Exponent Morrey Spaces

作　　者：杨沿奇 陶双平 Yan Qi YANG;Shuang Ping TAO(College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, P. R. China)

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《数学学报（中文版）》2019年第3期503-514,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11561062)

摘　　要：在满足一定的正则性假设条件下,建立了θ-型Calderón-Zygmund算子T_θ在一类变指数Lebesgue空间上的加权有界性.进一步得到了T_θ在加权变指数Herz空间和Herz-Morrey空间上的有界性.另外,还证明了相应的交换子[b,T_θ]在广义加权变指数Morrey空间上是有界的.We obtain some boundedness results for the θ-type Calderón-Zygmund operators Tθ under natural regularity assumptions on a class of generalized Lebesgue spaces with weight and variable exponent. Furthermore, the boundedness of Tθ is established on the weighted variable Herz and Herz-Morrey spaces based on the above conclusions. We also prove the boundedness of the corresponding commutator [b,Tθ]in the generalized weighted Morrey spaces with variable exponent.

关 键 词：θ-型Calderón-Zygmund算子 加权变指数Morrey空间 加权变指数Herz-Morrey空间 

分 类 号：O174.2[理学—数学]