## 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 ≤ 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) |
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Pages (from-to) | 1427-1435 |

Number of pages | 9 |

Journal | Proceedings of the American Mathematical Society |

Volume | 127 |

Issue number | 5 |

DOIs | |

State | Published - 1999 |

Externally published | Yes |

## Keywords

- H function
- Tube submanifold

## ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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