The holomorphic extension of Hp-CR functions on tube submanifolds

Al Boggess

doi:10.1090/s0002-9939-99-04828-5

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

Al Boggess

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

We consider the set of CR functions on a connected tube submanifold of Cⁿ 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 ≤ p ≤ ∞). 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.

Original language	English (US)
Pages (from-to)	1427-1435
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	127
Issue number	5
DOIs	https://doi.org/10.1090/s0002-9939-99-04828-5
State	Published - 1999
Externally published	Yes

Keywords

H function
Tube submanifold

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Access to Document

10.1090/s0002-9939-99-04828-5

Cite this

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abstract = "We consider the set of CR functions on a connected tube submanifold of Cn satisfying a uniform bound on the Lp-norm in the tube direction. We show that all such CR functions holomorphically extend to Hp functions on the convex hull of the tube (1 ≤ p ≤ ∞). The Hp-norm of the extension is shown to be the same as the uniform Lp-norm in the tube direction of the CR function.",

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AB - We consider the set of CR functions on a connected tube submanifold of Cn satisfying a uniform bound on the Lp-norm in the tube direction. We show that all such CR functions holomorphically extend to Hp functions on the convex hull of the tube (1 ≤ p ≤ ∞). The Hp-norm of the extension is shown to be the same as the uniform Lp-norm in the tube direction of the CR function.

KW - H function

KW - Tube submanifold

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DO - 10.1090/s0002-9939-99-04828-5

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

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