Weighted Norm Inequalities for Pluriharmonic Conjugate Functions

We define pluriharmonic conjugate functions on the unit ball of Cn. 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...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2002-04, Vol.268 (2), p.707-717
Main Authors: Lee, Jaesung, Soo Rim, Kyung
Format: Article
Language:English
Subjects:
Exact sciences and technology
Functional analysis
Mathematical analysis
Mathematics
pluriharmonic conjugate function
Sciences and techniques of general use
weighted norm inequality
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Summary:We define pluriharmonic conjugate functions on the unit ball of Cn. 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.
ISSN:0022-247X
1096-0813
DOI:10.1006/jmaa.2001.7731