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

 

The holomorphic extension of $H^p$-CR functions
on tube submanifolds


Author: Al Boggess
Journal: Proc. Amer. Math. Soc. 127 (1999), 1427-1435
MSC (1991): Primary 32A35, 42B30, 32D99
Published electronically: January 29, 1999
MathSciNet review: 1600104
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Abstract: We consider the set of CR functions on a connected tube submanifold of $C^n$ satisfying a uniform bound on the $L^p$-norm in the tube direction. We show that all such CR functions holomorphically extend to $H^p$ functions on the convex hull of the tube ($1 \leq p \leq \infty$). The $H^p$-norm of the extension is shown to be the same as the uniform $L^p$-norm in the tube direction of the CR function.


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Additional Information

Al Boggess
Affiliation: Department of Mathematics, Texas A & M University, College Station, Texas 77843
Email: al.boggess@math.tamu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04828-5
PII: S 0002-9939(99)04828-5
Keywords: $H^p$ function, tube submanifold
Received by editor(s): August 22, 1997
Published electronically: January 29, 1999
Communicated by: Steven R. Bell
Article copyright: © Copyright 1999 American Mathematical Society