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

页码：734 / 746

页数：13

共 12 条

[1]

Arcozzi N, 2011, NEW YORK J MATH, V17A, P45

[2]

Carroll T., 1991, J. Operator Theory, V26, P109

[3]

Cowen C. C., 1994, COMPOSITION OPERATOR

[4] Level sets and composition operators on the Dirichlet space [J].