Differences of composition operators on weighted Bergman spaces

Ching on Lo; Anthony Wai keung Loh

doi:10.1007/s11587-021-00592-2

Differences of composition operators on weighted Bergman spaces

Division of Science, Engineering and Health Studies (SEHS)

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

Abstract

We obtain a new boundedness criterion for the difference of two composition operators from a weighted Bergman space Aαp into a Lebesgue space L^q(μ) , where 0 < q< p and α> - 1. As a consequence, we provide a direct proof that such a bounded difference operator is necessarily compact. We also characterize compact differences of composition operators from Aαp into Aβq explicitly for 0 < p≤ q and α, β> - 1.

Original language	English
Pages (from-to)	815-833
Number of pages	19
Journal	Ricerche di Matematica
Volume	72
Issue number	2
DOIs	https://doi.org/10.1007/s11587-021-00592-2
Publication status	Published - 8 May 2021

Keywords

Bounded
Compact
Composition operator
Difference
Weighted Bergman space

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10.1007/s11587-021-00592-2

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author = "Lo, \{Ching on\} and Loh, \{Anthony Wai keung\}",

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T1 - Differences of composition operators on weighted Bergman spaces

AU - Lo, Ching on

AU - Loh, Anthony Wai keung

PY - 2021/5/8

Y1 - 2021/5/8

N2 - We obtain a new boundedness criterion for the difference of two composition operators from a weighted Bergman space Aαp into a Lebesgue space Lq(μ) , where 0 < q< p and α> - 1. As a consequence, we provide a direct proof that such a bounded difference operator is necessarily compact. We also characterize compact differences of composition operators from Aαp into Aβq explicitly for 0 < p≤ q and α, β> - 1.

AB - We obtain a new boundedness criterion for the difference of two composition operators from a weighted Bergman space Aαp into a Lebesgue space Lq(μ) , where 0 < q< p and α> - 1. As a consequence, we provide a direct proof that such a bounded difference operator is necessarily compact. We also characterize compact differences of composition operators from Aαp into Aβq explicitly for 0 < p≤ q and α, β> - 1.

KW - Bounded

KW - Compact

KW - Composition operator

KW - Difference

KW - Weighted Bergman space

UR - https://www.scopus.com/pages/publications/85105433675

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EP - 833

JO - Ricerche di Matematica

JF - Ricerche di Matematica

IS - 2

ER -

Differences of composition operators on weighted Bergman spaces

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