Essential norm estimates for composition operators on BMOA

Pablo Galindo; Jussi Laitila; Mikael Lindström

doi:10.1016/j.jfa.2013.05.002

Essential norm estimates for composition operators on BMOA

Pablo Galindo^*, Jussi Laitila, Mikael Lindström

^*Corresponding author for this work

Mathematics

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

17 Citations (Scopus)

Abstract

We provide two function-theoretic estimates for the essential norm of a composition operator C_φ acting on the space BMOA; one in terms of the n-th power φⁿ of the symbol φ and one which involves the Nevanlinna counting function. We also show that if the symbol φ is univalent, then the essential norm of C_φ is comparable to its essential norm on the Bloch space.

Original language	English
Pages (from-to)	629-643
Number of pages	15
Journal	Journal of Functional Analysis
Volume	265
Issue number	4
DOIs	https://doi.org/10.1016/j.jfa.2013.05.002
Publication status	Published - 15 Aug 2013
MoE publication type	A1 Journal article-refereed

Keywords

BMOA
Bounded mean oscillation
Compactness
Composition operator
Essential norm
VMOA

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10.1016/j.jfa.2013.05.002

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AU - Laitila, Jussi

AU - Lindström, Mikael

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N2 - We provide two function-theoretic estimates for the essential norm of a composition operator Cφ acting on the space BMOA; one in terms of the n-th power φn of the symbol φ and one which involves the Nevanlinna counting function. We also show that if the symbol φ is univalent, then the essential norm of Cφ is comparable to its essential norm on the Bloch space.

AB - We provide two function-theoretic estimates for the essential norm of a composition operator Cφ acting on the space BMOA; one in terms of the n-th power φn of the symbol φ and one which involves the Nevanlinna counting function. We also show that if the symbol φ is univalent, then the essential norm of Cφ is comparable to its essential norm on the Bloch space.

KW - BMOA

KW - Bounded mean oscillation

KW - Compactness

KW - Composition operator

KW - Essential norm

KW - VMOA

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JO - Journal of Functional Analysis

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Essential norm estimates for composition operators on BMOA

Abstract

Keywords

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