Dirichlet problem in Lipschitz domains with BMO data

Authors:
Eugene B. Fabes and Umberto Neri

Journal:
Proc. Amer. Math. Soc. **78** (1980), 33-39

MSC:
Primary 31B05; Secondary 31B25

MathSciNet review:
548079

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Abstract: In any bounded starlike Lipschitz domain, the harmonic functions whose boundary values are in BMO (the class of functions with bounded mean oscillation) of the boundary are shown to be characterized by the property that their Littlewood-Paley measures are Carleson measures. This result extends the analogous characterization found by the authors when the domain in question is a half-space.

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DOI:
https://doi.org/10.1090/S0002-9939-1980-0548079-8

Article copyright:
© Copyright 1980
American Mathematical Society