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.