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

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.