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Relating composition operators on different weighted Hardy spaces

✍ Scribed by Paul R. Hurst

Publisher
Springer
Year
1997
Tongue
English
Weight
226 KB
Volume
68
Category
Article
ISSN
0003-889X

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Let , be analytic functions defined on ‫,ބ‬ such that ‫ބ‬ : ‫.ބ‬ The operator Ε½ . given by f Β¬ f ( is called a weighted composition operator. In this paper we deal with the boundedness, compactness, weak compactness, and complete continu-Ε½ . 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^(__Ξ²__). For any bounded weight sequence __Ξ²__, 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