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Volume 30, Issue 2
Weighted Composition Operators from the Bloch Space to Weighted Banach Spaces on Bounded Homogeneous Domains

R. F. Allen

DOI: 10.4208/ata.2014.v30.n2.9

Anal. Theory Appl., 30 (2014), pp. 236-248.

Published online: 2014-06

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  • Abstract

We study the bounded and the compact weighted composition operators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded homogeneous domains, with particular attention to the unit polydisk. For bounded homogeneous domains, we characterize the bounded weighted composition operators and determine the operator norm. In addition, we provide sufficient conditions for compactness. For the unit polydisk, we completely characterize the compact weighted composition operators, as well as provide "computable" estimates on the operator norm.

  • Keywords

Weighted composition operators, Bloch space, weighted Banach space, homogeneous domain.

  • AMS Subject Headings

47B38, 32A18

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-30-236, author = {}, title = {Weighted Composition Operators from the Bloch Space to Weighted Banach Spaces on Bounded Homogeneous Domains}, journal = {Analysis in Theory and Applications}, year = {2014}, volume = {30}, number = {2}, pages = {236--248}, abstract = {

We study the bounded and the compact weighted composition operators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded homogeneous domains, with particular attention to the unit polydisk. For bounded homogeneous domains, we characterize the bounded weighted composition operators and determine the operator norm. In addition, we provide sufficient conditions for compactness. For the unit polydisk, we completely characterize the compact weighted composition operators, as well as provide "computable" estimates on the operator norm.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2014.v30.n2.9}, url = {http://global-sci.org/intro/article_detail/ata/4488.html} }
TY - JOUR T1 - Weighted Composition Operators from the Bloch Space to Weighted Banach Spaces on Bounded Homogeneous Domains JO - Analysis in Theory and Applications VL - 2 SP - 236 EP - 248 PY - 2014 DA - 2014/06 SN - 30 DO - http://doi.org/10.4208/ata.2014.v30.n2.9 UR - https://global-sci.org/intro/article_detail/ata/4488.html KW - Weighted composition operators, Bloch space, weighted Banach space, homogeneous domain. AB -

We study the bounded and the compact weighted composition operators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded homogeneous domains, with particular attention to the unit polydisk. For bounded homogeneous domains, we characterize the bounded weighted composition operators and determine the operator norm. In addition, we provide sufficient conditions for compactness. For the unit polydisk, we completely characterize the compact weighted composition operators, as well as provide "computable" estimates on the operator norm.

R. F. Allen. (1970). Weighted Composition Operators from the Bloch Space to Weighted Banach Spaces on Bounded Homogeneous Domains. Analysis in Theory and Applications. 30 (2). 236-248. doi:10.4208/ata.2014.v30.n2.9
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