Hausdorff Operators on Function Spaces  

作　　者：Jiecheng CHEN Dashan FAN Jun LI 

机构地区：[1]Department of Mathematics, Zt~ejiang Normal University, Jinhua 321004, China Department of Mathematics, Zhejiang University, Hangzhou 310027, China [2]Department of Mathematics, University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA. [3]Department of Mathematics, Zhejiang University, Hangzhou 310027, China.

出　　处：《Chinese Annals of Mathematics,Series B》2012年第4期537-556,共20页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China (Nos. 10931001, 10871173)

摘　　要：The authors mainly study the Hausdorff operators on Euclidean space Rn. They establish boundedness of the Hausdorff operators in various function spaces, such as Lebesgue spaces, Hardy spaces, local Hardy spaces and Herz type spaces. The results reveal that the Hausdorff operators have better performance on the Herz type Hardy spaces HKP（Rn） than their performance on the Hardy spaces Hv（Rn） when 0 〈 p 〈 1. Also, the authors obtain some new results and reprove or generalize some known results for the high dimensional Hardy operator and adjoint Hardy operator.

关 键 词：Hausdorff operator Hardy operator Hardy space Herz space 

分 类 号：O175.5[理学—数学] O174.2[理学—基础数学]