Hiroshima Mathematical Journal

Composition operators on the Bergman spaces of a minimal bounded homogeneous domain

Satoshi Yamaji

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Abstract

Using an integral formula on a homogeneous Siegel domain, we give a necessary and sufficient condition for composition operators on the weighted Bergman space of a minimal bounded homogeneous domain to be compact in terms of a boundary behavior of the Bergman kernel.

Article information

Source
Hiroshima Math. J., Volume 43, Number 1 (2013), 107-128.

Dates
First available in Project Euclid: 10 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1368217952

Digital Object Identifier
doi:10.32917/hmj/1368217952

Mathematical Reviews number (MathSciNet)
MR3066527

Zentralblatt MATH identifier
1304.47034

Subjects
Primary: 47B33: Composition operators
Secondary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15] 32A25: Integral representations; canonical kernels (Szego, Bergman, etc.)

Keywords
Composition operator Bergman space bounded homogeneous domain minimal domain Carleson measure

Citation

Yamaji, Satoshi. Composition operators on the Bergman spaces of a minimal bounded homogeneous domain. Hiroshima Math. J. 43 (2013), no. 1, 107--128. doi:10.32917/hmj/1368217952. https://projecteuclid.org/euclid.hmj/1368217952


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