Compactness of operators on the bergman space of the thullen domain

Zhenghui Huo; Brett D. Wick

doi:10.7900/jot.2018oct16.2216

Compactness of operators on the bergman space of the thullen domain

Zhenghui Huo
, Brett D. Wick

Department of Mathematics

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

2 Scopus citations

Abstract

We study compact operators on the Bergman space of the domain defined by [(z₁, z₂) ε[lunate] ²: [divides]z₁[divides]^2p + [divides]z₂[divides]² < 1] with p > 0 and p 6= 1. The domain need not be smooth nor have a transitive automorphism group. We give a sufficient condition for the boundedness of various operators on the Bergman space. Under this boundedness condition, we characterize the compactness of operators on the Bergman space of the Thullen domain.

Original language	English
Pages (from-to)	391-421
Number of pages	31
Journal	Journal of Operator Theory
Volume	83
Issue number	2
DOIs	https://doi.org/10.7900/jot.2018oct16.2216
State	Published - Mar 1 2020

Keywords

Bergman space
Compact operator
Thullen domain
Toeplitz operator

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abstract = "We study compact operators on the Bergman space of the domain defined by [(z1, z2) ε[lunate] 2: [divides]z1[divides]2p + [divides]z2[divides]2 < 1] with p > 0 and p 6= 1. The domain need not be smooth nor have a transitive automorphism group. We give a sufficient condition for the boundedness of various operators on the Bergman space. Under this boundedness condition, we characterize the compactness of operators on the Bergman space of the Thullen domain.",

keywords = "Bergman space, Compact operator, Thullen domain, Toeplitz operator",

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doi = "10.7900/jot.2018oct16.2216",

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AU - Huo, Zhenghui

AU - Wick, Brett D.

N1 - Publisher Copyright: © Copyright by THETA, 2020.

PY - 2020/3/1

Y1 - 2020/3/1

N2 - We study compact operators on the Bergman space of the domain defined by [(z1, z2) ε[lunate] 2: [divides]z1[divides]2p + [divides]z2[divides]2 < 1] with p > 0 and p 6= 1. The domain need not be smooth nor have a transitive automorphism group. We give a sufficient condition for the boundedness of various operators on the Bergman space. Under this boundedness condition, we characterize the compactness of operators on the Bergman space of the Thullen domain.

AB - We study compact operators on the Bergman space of the domain defined by [(z1, z2) ε[lunate] 2: [divides]z1[divides]2p + [divides]z2[divides]2 < 1] with p > 0 and p 6= 1. The domain need not be smooth nor have a transitive automorphism group. We give a sufficient condition for the boundedness of various operators on the Bergman space. Under this boundedness condition, we characterize the compactness of operators on the Bergman space of the Thullen domain.

KW - Bergman space

KW - Compact operator

KW - Thullen domain

KW - Toeplitz operator

UR - https://www.scopus.com/pages/publications/85088276060

U2 - 10.7900/jot.2018oct16.2216

DO - 10.7900/jot.2018oct16.2216

M3 - Article

AN - SCOPUS:85088276060

SN - 0379-4024

VL - 83

SP - 391

EP - 421

JO - Journal of Operator Theory

JF - Journal of Operator Theory

IS - 2

ER -

Compactness of operators on the bergman space of the thullen domain

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