Advanced Studies in Pure Mathematics

Harmonic conjugates of parabolic Bergman functions

Masahiro Yamada

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Abstract

The parabolic Bergman space is the Banach space of solutions of some parabolic equations on the upper half space which have finite $L^p$ norms. We introduce and study $L^{(\alpha)}$-harmonic conjugates of parabolic Bergman functions, and give a sufficient condition for a parabolic Bergman space to have unique $L^{(\alpha)}$-harmonic conjugates.

Article information

Source
Potential Theory in Matsue, H. Aikawa, T. Kumagai, Y. Mizuta and N. Suzuki, eds. (Tokyo: Mathematical Society of Japan, 2006), 391-402

Dates
Received: 2 March 2005
Revised: 16 May 2005
First available in Project Euclid: 16 December 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1544999706

Digital Object Identifier
doi:10.2969/aspm/04410391

Mathematical Reviews number (MathSciNet)
MR2279771

Zentralblatt MATH identifier
1120.35042

Subjects
Primary: 32A36: Bergman spaces
Secondary: 26D10: Inequalities involving derivatives and differential and integral operators 35K05: Heat equation

Keywords
Bergman space harmonic conjugate heat equation parabolic equation

Citation

Yamada, Masahiro. Harmonic conjugates of parabolic Bergman functions. Potential Theory in Matsue, 391--402, Mathematical Society of Japan, Tokyo, Japan, 2006. doi:10.2969/aspm/04410391. https://projecteuclid.org/euclid.aspm/1544999706


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