Schatten class Toeplitz operators on the parabolic Bergman space II

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Author(s)

Abstract

Let 0 < α ≤ 1 and let <b><i>b</i></b><sup>2</sup><sub>α</sub> be a Hilbert space of all square integrable solutions of a parabolic equation (∂<sub><i>t</i></sub> + (−Δ)<sup>α</sup>)<i>u</i> = 0 on the upper half space. We study the Toeplitz operators on <b><i>b</i></b><sup>2</sup><sub>α</sub>, which we characterize to be of Schatten class whose exponent is smaller than 1. For the proof, we use an atomic decomposition theorem of parabolic Bergman functions. Generalizations to Schatten class operators for Orlicz type and Herz type are also discussed.

Journal

  • Kodai Mathematical Journal

    Kodai Mathematical Journal 35(1), 52-77, 2012

    Department of Mathematics, Tokyo Institute of Technology

Codes

  • NII Article ID (NAID)
    130004496158
  • Text Lang
    ENG
  • ISSN
    0386-5991
  • Data Source
    J-STAGE 
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