Integral Operators Between Fock Spaces

作     者：Yongqing LIU Shengzhao HOU Yongqing LIU;Shengzhao HOU

作者机构：School of Mathematics and StatisticsChangshu Institute of TechnologySuzhou 215006JiangsuChina School of Mathematical SciencesSoochow UniversitySuzhou 215006JiangsuChina 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2024年第45卷第2期

页      面：265-278页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China(No.11971340) 

主　　题：Fock spaces Integral operators Normalized reproducing kernel 

摘      要：In this paper,the authors study the integral operator■induced by a kernel functionφ(z,·)∈F_α~∞between Fock *** 1≤p≤∞,they prove that S_φ:F_α^(1)→F_α^(p)is bounded if and only if■where k_(a)is the normalized reproducing kernel of F_α^(2);and,S_φ:F_α^(1)→F_α^(p)is compact if and only if■When 1q≤∞,it is also proved that the condition(?)is not sufficient for boundedness of S_φ:F_α^(q)→F_α^(p).In the particular case■with ■∈F^(2)_α,for 1≤qp∞,they show that S_φ:F^(p)_α→F^(q)_αis bounded if and only if■;for 1p≤q∞,they give sufficient conditions for the boundedness or compactness of the operator S^(q)_φ:F^(p)_α→F_α.