Difference of Weighted Composition Operators Over the Ball

Boo Rim Choe; Koeun Choi; Hyung Woon Koo; Inyoung Park

doi:10.1007/s11785-023-01477-y

Difference of Weighted Composition Operators Over the Ball

Boo Rim Choe
, Koeun Choi^*
, Hyung Woon Koo
, Inyoung Park

^*Corresponding author for this work

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

3 Citations (Scopus)

Abstract

Recently, Choe et al. obtained characterizations for bounded/compact differences of weighted composition operators acting from a standard weighted Bergman space into another over the unit disk. In this paper we extend those results to the ball setting. By devising a new approach regarding test functions, we improve the characterizations as well as the proofs. Namely, the Reproducing Kernel Thesis is added to the characterizations and our proofs, when restricted to the disk, are new and simpler.

Original language	English
Article number	33
Journal	Complex Analysis and Operator Theory
Volume	18
Issue number	2
DOIs	https://doi.org/10.1007/s11785-023-01477-y
Publication status	Published - 2024 Feb

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.

Keywords

Bergman space
Boundedness
Carleson measure
Compactness
Difference
Primary 47B33
Reproducing Kernel Thesis
Secondary 32A36
Weighted composition operator

ASJC Scopus subject areas

Computational Mathematics
Computational Theory and Mathematics
Applied Mathematics

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10.1007/s11785-023-01477-y

Cite this

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title = "Difference of Weighted Composition Operators Over the Ball",

abstract = "Recently, Choe et al. obtained characterizations for bounded/compact differences of weighted composition operators acting from a standard weighted Bergman space into another over the unit disk. In this paper we extend those results to the ball setting. By devising a new approach regarding test functions, we improve the characterizations as well as the proofs. Namely, the Reproducing Kernel Thesis is added to the characterizations and our proofs, when restricted to the disk, are new and simpler.",

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author = "Choe, \{Boo Rim\} and Koeun Choi and Koo, \{Hyung Woon\} and Inyoung Park",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.",

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doi = "10.1007/s11785-023-01477-y",

language = "English",

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T1 - Difference of Weighted Composition Operators Over the Ball

AU - Choe, Boo Rim

AU - Choi, Koeun

AU - Koo, Hyung Woon

AU - Park, Inyoung

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.

PY - 2024/2

Y1 - 2024/2

N2 - Recently, Choe et al. obtained characterizations for bounded/compact differences of weighted composition operators acting from a standard weighted Bergman space into another over the unit disk. In this paper we extend those results to the ball setting. By devising a new approach regarding test functions, we improve the characterizations as well as the proofs. Namely, the Reproducing Kernel Thesis is added to the characterizations and our proofs, when restricted to the disk, are new and simpler.

AB - Recently, Choe et al. obtained characterizations for bounded/compact differences of weighted composition operators acting from a standard weighted Bergman space into another over the unit disk. In this paper we extend those results to the ball setting. By devising a new approach regarding test functions, we improve the characterizations as well as the proofs. Namely, the Reproducing Kernel Thesis is added to the characterizations and our proofs, when restricted to the disk, are new and simpler.

KW - Bergman space

KW - Boundedness

KW - Carleson measure

KW - Compactness

KW - Difference

KW - Primary 47B33

KW - Reproducing Kernel Thesis

KW - Secondary 32A36

KW - Weighted composition operator

UR - https://www.scopus.com/pages/publications/85187195443

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DO - 10.1007/s11785-023-01477-y

M3 - Article

AN - SCOPUS:85187195443

SN - 1661-8254

VL - 18

JO - Complex Analysis and Operator Theory

JF - Complex Analysis and Operator Theory

IS - 2

M1 - 33

ER -

Difference of Weighted Composition Operators Over the Ball

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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