Weighted norm inequalities for pluriharmonic conjugate functions

초록

We define pluriharmonic conjugate functions on the unit ball of C-n. Then we show that for a weight there exist weighted norm inequalities for pluriharmonic conjugate functions on L-p if and only if the weight satisfies the A(p)-condition. As an application, we prove the equivalence of the weighted norm inequalities for the Cauchy integral and the A(p)-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. (C) 2002 Elsevier Science (USA).

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