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Composition Operators on Hardy–Orlicz Spaces on the Ball

✍ Scribed by Stéphane Charpentier

Publisher
SP Birkhäuser Verlag Basel
Year
2011
Tongue
English
Weight
344 KB
Volume
70
Category
Article
ISSN
0378-620X

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Let , be analytic functions defined on ‫,ބ‬ such that ‫ބ‬ : ‫.ބ‬ The operator Ž . given by f ¬ f ( is called a weighted composition operator. In this paper we deal with the boundedness, compactness, weak compactness, and complete continu-Ž . ity of weighted composition operators on Hardy spaces H 1

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## Abstract We investigate the composition operators on the weighted Hardy spaces __H__^2^(__β__). For any bounded weight sequence __β__, we give necessary conditions for those operators to be isometric. The sufficiency of those conditions is well‐known for the classical space __H__^2^. In the case