Open Access
March 2012 Schatten class Toeplitz operators on the parabolic Bergman space II
Masaharu Nishio, Noriaki Suzuki, Masahiro Yamada
Kodai Math. J. 35(1): 52-77 (March 2012). DOI: 10.2996/kmj/1333027254


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.


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Masaharu Nishio. Noriaki Suzuki. Masahiro Yamada. "Schatten class Toeplitz operators on the parabolic Bergman space II." Kodai Math. J. 35 (1) 52 - 77, March 2012.


Published: March 2012
First available in Project Euclid: 29 March 2012

zbMATH: 1243.35076
MathSciNet: MR2911266
Digital Object Identifier: 10.2996/kmj/1333027254

Rights: Copyright © 2012 Tokyo Institute of Technology, Department of Mathematics

Vol.35 • No. 1 • March 2012
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