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Weighted Norm Inequalities for Pluriharmonic Conjugate Functions

✍ Scribed by Jaesung Lee; Kyung Soo Rim

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 97 KB
Volume: 268
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.2001.7731

No coin nor oath required. For personal study only.

✦ Synopsis

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 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.  2002 Elsevier Science (USA)

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