Journal of the Mathematical Society of Japan

Positive Toeplitz operators on weighted Bergman spaces of a minimal bounded homogeneous domain

Satoshi YAMAJI

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Abstract

We give criteria for the boundedness of positive Toeplitz operators on weighted Bergman spaces of a minimal bounded homogeneous domain in terms of the Berezin symbol or the averaging function of the symbol. Moreover, we estimate the essential norm of positive Toeplitz operators assuming that they are bounded. As an application of these estimates, we also give necessary and sufficient conditions for the positive Toeplitz operators to be compact.

Article information

Source
J. Math. Soc. Japan, Volume 65, Number 4 (2013), 1101-1115.

Dates
First available in Project Euclid: 24 October 2013

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1382620187

Digital Object Identifier
doi:10.2969/jmsj/06541101

Mathematical Reviews number (MathSciNet)
MR3127818

Zentralblatt MATH identifier
1284.47025

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

Keywords
Toeplitz operator essential norm Bergman space bounded homogeneous domain minimal domain

Citation

YAMAJI, Satoshi. Positive Toeplitz operators on weighted Bergman spaces of a minimal bounded homogeneous domain. J. Math. Soc. Japan 65 (2013), no. 4, 1101--1115. doi:10.2969/jmsj/06541101. https://projecteuclid.org/euclid.jmsj/1382620187


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