Journal of Mathematics of Kyoto University

Compact radial operators on the harmonic Bergman space

Young Joo Lee

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Abstract

We study the characterizing problem of the compactness of radial operators on the harmonic Bergman space. We show that under an oscillation condition, the compactness is equivalent to the boundary vanishing conditions of the certain Berezin transforms. As an application, we characterize compact Toeplitz operators with radial symbol on the harmonic Bergman space.

Article information

Source
J. Math. Kyoto Univ., Volume 44, Number 4 (2004), 769-777.

Dates
First available in Project Euclid: 14 August 2009

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1250281697

Digital Object Identifier
doi:10.1215/kjm/1250281697

Mathematical Reviews number (MathSciNet)
MR2118040

Subjects
Primary: 47B38: Operators on function spaces (general)
Secondary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]

Citation

Lee, Young Joo. Compact radial operators on the harmonic Bergman space. J. Math. Kyoto Univ. 44 (2004), no. 4, 769--777. doi:10.1215/kjm/1250281697. https://projecteuclid.org/euclid.kjm/1250281697


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