p-Bloch空间上的复合算子和加权复合算子  

THE COMPOSITION OPERATORS AND WEIGHTED COMPOSITION OPERATORS ON p-BLOCH SPACES

作　　者：张学军[1] 

机构地区：[1]湖南师范大学数学与计算机科学学院数学系,长沙410006

出　　处：《数学年刊（A辑）》2003年第6期711-720,共10页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.19871026)基金资助的项目

摘　　要：本文系统地讨论了单位圆中p-Bloch空间上复合算子T1,δ的有界性和紧性以及加权复合算子Tφ,δ的有界性,同时也在小p-Bloch空间上讨论了复合算子T1,φ的有界性问题.主要得到以下结论: (i)Tφ,δ是空间βp到βq的有界算子之充要条件; (ii)T1,φ是空间βp到βq的紧算子之充要条件; (iii)T1,φ是空间βp0到βq0的有界算子之充要条件等.从空间或算子上扩展了文[1,4]的相应结论.This paper discusses the boundedness and compactness of compsition operators T1,φ and weighted composition operators Tφ,φ between the p-Bloch spaces on the unit disc. At the same time, the author studies the boundedness of T^ between the little p-Bloch spaces. It is obtained as follows: (i) the sufficient and necessary conditions of Tφ,φ being bounded operators from spaces βP to βq (ii) the sufficient and necessary conditions of T1,φ being compact operators from spaces βpto βq; (iii) the sufficient and necessary conditions of T1,φ being bounded operators from spaces βp0 to βq0. These results generalized the corresponding results of Madigan and Matheson, Ohno and Zhao.

关 键 词：有界性 加权复合算子 P-BLOCH空间 单位圆 点乘子 

分 类 号：O177[理学—数学]