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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

An extension theorem for $H^{p}$ functions


Author: Joseph A. Cima
Journal: Proc. Amer. Math. Soc. 42 (1974), 529-532
MSC: Primary 32D20; Secondary 30A78
DOI: https://doi.org/10.1090/S0002-9939-1974-0326003-8
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 $|f(z){|^p} \leqq u(z)$ for $z \in \Omega$. Then f can be analytically extended to a function $\hat f$ in ${H^p}({U^n})$.


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Keywords: Polyharmonic, <IMG WIDTH="33" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${H^p}$">, polydisc, analytic
Article copyright: © Copyright 1974 American Mathematical Society