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Volume 32, Issue 3
Closed Range Composition Operators on a General Family of Function Spaces

M. A. Bakhit

Anal. Theory Appl., 32 (2016), pp. 215-231.

Published online: 2016-07

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  • Abstract

In this paper, necessary and sufficient conditions for a closed range composition operator $C_{\phi}$ on the general family of holomorphic function spaces $F(p, q, s)$ and more generally on $\alpha$-Besov type spaces $F(p, \alpha p-2, s)$ are given. We give a Carleson measure characterization on $F(p, \alpha p-2, s)$ spaces, then we indicate how Carleson measures can be used to characterize boundedness and compactness of $C_{\phi}$ on $F(p,q,s)$ and $F(p,\alpha p-2,s)$ spaces.

  • AMS Subject Headings

47B33, 47B38, 30H25, 30H30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-32-215, author = {M. A. Bakhit}, title = {Closed Range Composition Operators on a General Family of Function Spaces}, journal = {Analysis in Theory and Applications}, year = {2016}, volume = {32}, number = {3}, pages = {215--231}, abstract = {

In this paper, necessary and sufficient conditions for a closed range composition operator $C_{\phi}$ on the general family of holomorphic function spaces $F(p, q, s)$ and more generally on $\alpha$-Besov type spaces $F(p, \alpha p-2, s)$ are given. We give a Carleson measure characterization on $F(p, \alpha p-2, s)$ spaces, then we indicate how Carleson measures can be used to characterize boundedness and compactness of $C_{\phi}$ on $F(p,q,s)$ and $F(p,\alpha p-2,s)$ spaces.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2016.v32.n3.2}, url = {http://global-sci.org/intro/article_detail/ata/4667.html} }
TY - JOUR T1 - Closed Range Composition Operators on a General Family of Function Spaces AU - M. A. Bakhit JO - Analysis in Theory and Applications VL - 3 SP - 215 EP - 231 PY - 2016 DA - 2016/07 SN - 32 DO - http://doi.org/10.4208/ata.2016.v32.n3.2 UR - https://global-sci.org/intro/article_detail/ata/4667.html KW - Composition operators, $F(p,q,s)$ spaces, closed range, Carleson measure, Bloch space, Bergman type space. AB -

In this paper, necessary and sufficient conditions for a closed range composition operator $C_{\phi}$ on the general family of holomorphic function spaces $F(p, q, s)$ and more generally on $\alpha$-Besov type spaces $F(p, \alpha p-2, s)$ are given. We give a Carleson measure characterization on $F(p, \alpha p-2, s)$ spaces, then we indicate how Carleson measures can be used to characterize boundedness and compactness of $C_{\phi}$ on $F(p,q,s)$ and $F(p,\alpha p-2,s)$ spaces.

M. A. Bakhit. (2016). Closed Range Composition Operators on a General Family of Function Spaces. Analysis in Theory and Applications. 32 (3). 215-231. doi:10.4208/ata.2016.v32.n3.2
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