## Advanced Studies in Pure Mathematics

### Harmonic conjugates of parabolic Bergman functions

#### 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

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

https://projecteuclid.org/ euclid.aspm/1544999706

Digital Object Identifier
doi:10.2969/aspm/04410391

Mathematical Reviews number (MathSciNet)
MR2279771

Zentralblatt MATH identifier
1120.35042

#### 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