The holomorphic extension of -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 | References | Similar Articles | Additional Information

Abstract: We consider the set of CR functions on a connected tube submanifold of satisfying a uniform bound on the -norm in the tube direction. We show that all such CR functions holomorphically extend to functions on the convex hull of the tube (). The -norm of the extension is shown to be the same as the uniform -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:
https://doi.org/10.1090/S0002-9939-99-04828-5

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