Kodai Mathematical Journal

Schatten class Toeplitz operators on the parabolic Bergman space II

Masaharu Nishio, Noriaki Suzuki, and Masahiro Yamada

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Abstract

Let 0 < α ≤ 1 and let $\boldsymbol{b}_\alpha^{2}$ be a Hilbert space of all square integrable solutions of a parabolic equation (∂t + (−Δ)α)u = 0 on the upper half space. We study the Toeplitz operators on $\boldsymbol{b}_\alpha^{2}$, 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.

Article information

Source
Kodai Math. J., Volume 35, Number 1 (2012), 52-77.

Dates
First available in Project Euclid: 29 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1333027254

Digital Object Identifier
doi:10.2996/kmj/1333027254

Mathematical Reviews number (MathSciNet)
MR2911266

Zentralblatt MATH identifier
1243.35076

Citation

Nishio, Masaharu; Suzuki, Noriaki; Yamada, Masahiro. Schatten class Toeplitz operators on the parabolic Bergman space II. Kodai Math. J. 35 (2012), no. 1, 52--77. doi:10.2996/kmj/1333027254. https://projecteuclid.org/euclid.kmj/1333027254


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