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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An extension theorem for $ H\sp{p}$ functions


Author: Joseph A. Cima
Journal: Proc. Amer. Math. Soc. 42 (1974), 529-532
MSC: Primary 32D20; Secondary 30A78
MathSciNet review: 0326003
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Abstract: Let V be a pure $ (n - 1)$-dimensional variety in the polydisc $ {U^n}$ with the distance from V to the torus $ {\text{II}^n}$ positive and assume f is analytic on $ \Omega \equiv {U^n}\backslash V$ Further let $ u(z)$ be the real part of a function g analytic on $ \Omega $ and assume $ \vert f(z){\vert^p} \leqq u(z)$ for $ z \in \Omega $. Then f can be analytically extended to a function $ \hat f$ in $ {H^p}({U^n})$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0326003-8
PII: S 0002-9939(1974)0326003-8
Keywords: Polyharmonic, $ {H^p}$, polydisc, analytic
Article copyright: © Copyright 1974 American Mathematical Society