Boundedness of Harmonic Conjugation on Weighted Bergman Spaces

Abstract

We prove that if a weight is a Bekollé-Bonami weight for some $q$ and it satisfies another simple condition that depends on $0<p<\infty$, then the operator taking a function to its harmonic conjugate is bounded on the harmonic Bergman space $a^p$. One part of our results uses a certain special type of good lambda inequality.

10 pages