积分估计和加权Lebesgue空间上广义Forelli-Rudin型算子的有界性  

Integral estimates and the boundedness of the generalized Forelli-Rudin type operator on weighted Lebesgue spaces

作　　者：张学军 郭雨婷 陈洪欣 Xuejun Zhang;Yuting Guo;Hongxin Chen

机构地区：[1]湖南师范大学数学与统计学院,长沙410006

出　　处：《中国科学：数学》2023年第10期1357-1376,共20页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11942109);湖南省自然科学基金(批准号:2022JJ30369)资助项目。

摘　　要：本文给出当p≥1时加权Lebesgue空间Lp(Bn,dvt)上广义Forelli-Rudin型算子Sλ,τ,c,k,k′有界的充要条件,部分推广了Zhao和Zhou(2022)的结果.同时,为了证明主要结果,本文给出球面和球体上几个积分的双向估计,推广了Rudin(1980)的相应结果.In this paper,we give necessary and sufficient conditions of boundedness for the generalized Forelli-Rudin type operator S;;c;k;k′on the weighted Lebesgue space Lp(Bn;dvt)for p>1,which partially generalize the recent results of Zhao and Zhou(2022).At the same time,to prove the main results,we give bidirectional estimates of several integrals on the unit sphere and the unit ball for all cases,and generalize the corresponding results in Rudin’s monograph.

关 键 词：广义Forelli-Rudin型算子 加权Lebesgue空间 积分估计 有界性 

分 类 号：O177[理学—数学]