Two results on composition operators on the Dirichlet space

被引：6
|
作者：
Li, Daniel [1 ,2 ]
Queffelec, Herve [3 ,4 ]
Rodriguez-Piazza, Luis [5 ,6 ]
机构：
[1] Univ Lille Nord France, U Artois, Lab Math Lens EA 2462, F-62300 Lens, France
[2] Fac Sci Jean Perrin, Federat CNRS Nord Pas de Calais FR 2956, F-62300 Lens, France
[3] Univ Lille Nord France, USTL, Lab Paul Painleve UMR CNRS 8524, F-59655 Villeneuve Dascq, France
[4] Federat CNRS Nord Pas de Calais FR 2956, F-59655 Villeneuve Dascq, France
[5] Univ Seville, Fac Matemat, Dept Anal Matemat, E-41080 Seville, Spain
[6] IMUS, Seville 41080, Spain
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2015年 / 426卷 / 02期
关键词：
Approximation numbers; Carleson embedding; Composition operator; Cusp map; Dirichlet space; COMPACT COMPOSITION OPERATORS; BERGMAN SPACES;
D O I：
10.1016/j.jmaa.2015.01.062
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We show that the decay of approximation numbers of compact composition operators on the Dirichlet space D can be as slow as we wish. We also prove the optimality of a result of O. El-Fallah, K. Kellay, M. Shabankhah and H. Youssfi on boundedness on 7, of self-maps of the disk all of whose powers are norm-bounded in D. (C) 2015 Elsevier Inc. All rights reserved.
引用
收藏
页码：734 / 746
页数：13
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