The holomorphic extension of $H^p$-CR functions on tube submanifolds
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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.References
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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
- Received by editor(s): August 22, 1997
- Published electronically: January 29, 1999
- Communicated by: Steven R. Bell
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 1427-1435
- MSC (1991): Primary 32A35, 42B30, 32D99
- DOI: https://doi.org/10.1090/S0002-9939-99-04828-5
- MathSciNet review: 1600104