Schatten class composition operators on the Hardy space

被引：0
|
作者：
Yang, Wenwan [1 ]
Yuan, Cheng [1 ]
机构：
[1] Guangdong Univ Technol, Sch Math & Stat, Guangzhou 510520, Guangdong, Peoples R China
来源：
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 2023年
关键词：
composition operators; Hardy spaces; Schatten p-class; CONTACT POINTS; CRITERIA;
D O I：
10.1017/prm.2023.68
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Suppose 2 < p < infinity and phi is a holomorphic self-map of the open unit disk D. We show the following assertions: (1) If phi has bounded valence and integral (D)(1-|z|(2) / 1-|phi(z)|(2) ) (p/2) dA(Z)/(1 - |z|(2) < infinity, (0, 1) then C phi is in the Schatten p-class of the Hardy space H-2. (2) There exists a holomorphic self-map phi (which is, of course, not of bounded valence) such that the inequality (0.1) holds and C-phi : H-2 -> H-2 does not belong to the Schatten p-class.
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页数：14
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