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

Author(s): Al Boggess
Journal: Proc. Amer. Math. Soc. 127 (1999), 1427-1435.
MSC (1991): Primary 32A35, 42B30, 32D99
Posted: January 29, 1999
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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: 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
Posted: January 29, 1999
Communicated by: Steven R. Bell
Copyright of article: Copyright 1999, American Mathematical Society

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