Hausdorff Operators on the Heisenberg Group  

作　　者：Jiu Hua GUO Li Jing SUN Fa You ZHAO 

机构地区：[1]Department of Mathematics, Shanghai University [2]Department of Mathematical Sciences, University of Wisconsin-Milwaukee

出　　处：《Acta Mathematica Sinica,English Series》2015年第11期1703-1714,共12页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant No.11201287);China Scholarship Council(Grant No.201406895019)

摘　　要：This paper is devoted to the high-dimensional and multilinear Hausdorff operators on the Heisenberg group Hn. The sharp bounds for the strong type （p,p） （1 〈 p 〈 ∞） estimates of n- dimensional Hausdorff operators on Hn are obtained. The sharp bounds for strong （p,p） estimates are further extended to multilinear cases. As an application, we derive the sharp constant for the multilinear Hardy operator on Hn. The weak type （p,p） （1 〈 p 〈 ∞） estimates are also obtained.This paper is devoted to the high-dimensional and multilinear Hausdorff operators on the Heisenberg group Hn. The sharp bounds for the strong type （p,p） （1 〈 p 〈 ∞） estimates of n- dimensional Hausdorff operators on Hn are obtained. The sharp bounds for strong （p,p） estimates are further extended to multilinear cases. As an application, we derive the sharp constant for the multilinear Hardy operator on Hn. The weak type （p,p） （1 〈 p 〈 ∞） estimates are also obtained.

关 键 词：Hausdorff operator Heisenberg group MULTILINEAR sharp estimate 

分 类 号：O152[理学—数学]