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Closed Range Composition Operators on a General Family of Function Spaces

Closed Range Composition Operators on a General Family of Function Spaces

Year:    2016

Analysis in Theory and Applications, Vol. 32 (2016), Iss. 3 : pp. 215–231

Abstract

In this paper, necessary and sufficient conditions for a closed range composition operator Cϕ on the general family of holomorphic function spaces F(p,q,s) and more generally on α-Besov type spaces F(p,αp2,s) are given. We give a Carleson measure characterization on F(p,αp2,s) spaces, then we indicate how Carleson measures can be used to characterize boundedness and compactness of Cϕ on F(p,q,s) and F(p,αp2,s) spaces.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.2016.v32.n3.2

Analysis in Theory and Applications, Vol. 32 (2016), Iss. 3 : pp. 215–231

Published online:    2016-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Composition operators $F(p q s)$ spaces closed range Carleson measure Bloch space Bergman type space.