The holomorphic extension of Hp-CR functions on tube submanifolds

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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.

Original languageEnglish (US)
Pages (from-to)1427-1435
Number of pages9
JournalProceedings of the American Mathematical Society
Volume127
Issue number5
DOIs
StatePublished - 1999
Externally publishedYes

Keywords

  • H function
  • Tube submanifold

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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