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VOL. 44 | 2006 $L^p$-boundedness of Bergman projections for $\alpha$-parabolic operators
Masaharu Nishio, Katsunori Shimomura, Noriaki Suzuki

Editor(s) Hiroaki Aikawa, Takashi Kumagai, Yoshihiro Mizuta, Noriaki Suzuki

Abstract

We consider the $\alpha$-parabolic Bergman spaces on strip domains. The Bergman kernel is given by a series of derivatives of the fundamental solution. We prove the $L^p$-boundedness of the projection defined by the Bergman kernel and obtain the duality theorem for $1 \lt p \lt \infty$. At the same time, we give a new proof of the Huygens property, which enable us to verify all the results in [3] also for $n = 1$.

Information

Published: 1 January 2006
First available in Project Euclid: 16 December 2018

zbMATH: 1119.31006
MathSciNet: MR2277842

Digital Object Identifier: 10.2969/aspm/04410305

Subjects:
Primary: 31B10 , 35K05
Secondary: ‎46E15

Keywords: Bergman projection , Bergman space , Huygens property , parabolic operator of fractional order , reproducing kernel

Rights: Copyright © 2006 Mathematical Society of Japan

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