Bilinear Riesz means on the Heisenberg group  

作　　者：Heping Liu Min Wang 

机构地区：[1]School of Mathematical Sciences, Peking University

出　　处：《Science China Mathematics》2019年第12期2535-2556,共22页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11371036);supported by China Scholarship Council(Grant No.201606010026)

摘　　要：In this article, we investigate the bilinear Riesz means Sα associated with the sublaplacian on the Heisenberg group. We prove that the operator Sαis bounded from Lp1 × Lp2 into Lp for 1 p1, p2 ∞ and1/p = 1/p1 + 1/p2 when α is larger than the suitable smoothness index α（p1, p2）. There are some essential differences between the Euclidean space and the Heisenberg group for studying the bilinear Riesz means problem.We use some special techniques to obtain lower indices α（p1, p2）.In this article,we investigate the bilinear Riesz means S^α associated with the sublaplacian on the Heisenberg group.We prove that the operator S^α is bounded from L^P1×L^P2 into Lp for 1≤p1,P2≤∞ and 1/p=1/p1+l/p2 when a is larger than the suitable smoothness index α(p1,p2)-There are some essential differences bet ween the Euclidean space and the Heisenberg group for studying the bilinear Riesz means problem.We use some special techniques to obtain lower indices α(p1,p2).

关 键 词：HEISENBERG group BILINEAR RIESZ means RESTRICTION THEOREM 

分 类 号：O17[理学—数学]