Compact composition operators on Hardy-Orlicz and Bergman-Orlicz spaces

被引：10
|
作者：
Li, Daniel [1 ,2 ]
机构：
[1] Univ Lille Nord de France, F-59000 Lille, France
[2] Fac Sci Jean Perrin, UArtois, Lab Math Lens EA 2462, Federat CNRS Nord Pas de Calais FR 2956, F-62300 Lens, France
来源：
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS | 2011年 / 105卷 / 02期
关键词：
Bergman spaces; Bergman-Orlicz spaces; Blaschke product; Carleson function; Carleson measure; Compactness; Composition operator; Hardy spaces; Hardy-Orlicz spaces; Nevanlinna counting function;
D O I：
10.1007/s13398-011-0027-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is known, from results of MacCluer and Shapiro (Canad. J. Math. 38(4):878-906, 1986), that every composition operator which is compact on the Hardy space H-p, 1 <= p < infinity, is also compact on the Bergman space B-p = L-a(p)(D). In this survey, after having described the above known results, we consider Hardy-Orlicz H-Psi and Bergman-Orlicz B-Psi spaces, characterize the compactness of their composition operators, and show that there exist Orlicz functions for which there are composition operators which are compact on H-Psi but not on B-Psi.
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页码：247 / 260
页数：14
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