Weighted Norm Inequalities for Pluriharmonic Conjugate Functions

We define pluriharmonic conjugate functions on the unit ball of n. Then we show that for a weight there exist weighted norm inequalities for pluriharmonic conjugate functions on Lp if and only if the weight satisfies the Ap-condition. As an application, we prove the equivalence of the weighted norm inequalities for the Cauchy integral and the Ap-condition of the weight. Along the way, we show that there exist norm inequalities for pluriharmonic conjugate functions on BMO and on the nonisotropic Lipschitz spaces