Boundedness of Harmonic Conjugation on Weighted Bergman Spaces

We prove that if a weight is a Bekoll\'{e}-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.