Multilinear Hausdorff Operators and Their Best Constants  

作　　者：Jie Cheng CHEN Da Shan FAN Chun Jie ZHANG 

机构地区：[1]Department of Mathematics,Zhejiang Normal University [2]Department of Mathematics,Zhejiang University [3]Department of Mathematics,University of Wisconsin-Milwaukee,Milwaukee,WI53201,USA [4]School of Science,Hangzhou Dianzi University

出　　处：《Acta Mathematica Sinica,English Series》2012年第8期1521-1530,共10页数学学报（英文版）

基　　金：supported by NSF of China(Grant Nos.10931001,10871173);supported by NSF of China(Grant No.11026104)

摘　　要：In this paper, we study two different extensions of the Hausdorff operator to the multilinear case. Boundedness on Lebesgue spaces and Herz spaces is obtained. The bound on the Lebesgue space is optimal. Our results are substantial extensions of some known results on Multilinear high dimensional Hardy operator.In this paper, we study two different extensions of the Hausdorff operator to the multilinear case. Boundedness on Lebesgue spaces and Herz spaces is obtained. The bound on the Lebesgue space is optimal. Our results are substantial extensions of some known results on Multilinear high dimensional Hardy operator.

关 键 词：Hausdorff operator MULTILINEAR Herz space sharp bounds 

分 类 号：O177[理学—数学]