Estimates of essential norms of weighted composition operators between Bloch-type spaces

Olli Hyvärinen; Mikael Lindström

doi:10.1016/j.jmaa.2012.03.059

Estimates of essential norms of weighted composition operators between Bloch-type spaces

Olli Hyvärinen, Mikael Lindström^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › Scientific › peer-review

74 Citations (Scopus)

Abstract

We estimate the essential norm of weighted composition operators uC _φ acting on Bloch-type spacesBα in terms of the analytic function u:D→C and the n-th power of the analytic selfmapφ of the open unit discD. We obtain new characterizations for boundedness and compactness of uCφ:Bα→Bβ for all 0<α, β<∞, thus answering an open problem of Manhas and Zhao concerning the case α=1.

Original language	English
Pages (from-to)	38-44
Number of pages	7
Journal	Journal of Mathematical Analysis and Applications
Volume	393
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2012.03.059
Publication status	Published - 1 Sept 2012
MoE publication type	A1 Journal article-refereed

Keywords

Essential norm
Bloch-type spaces
Weighted composition operator

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10.1016/j.jmaa.2012.03.059

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AB - We estimate the essential norm of weighted composition operators uC φ acting on Bloch-type spacesBα in terms of the analytic function u:D→C and the n-th power of the analytic selfmapφ of the open unit discD. We obtain new characterizations for boundedness and compactness of uCφ:Bα→Bβ for all 0<α, β<∞, thus answering an open problem of Manhas and Zhao concerning the case α=1.

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Estimates of essential norms of weighted composition operators between Bloch-type spaces

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Keywords

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