### 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 |

State | Published - 1999 |

Externally published | Yes |

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### Keywords

- H function
- Tube submanifold

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**The holomorphic extension of H ^{p}-CR functions on tube submanifolds.** / Boggess, Albert.

Research output: Contribution to journal › Article

^{p}-CR functions on tube submanifolds',

*Proceedings of the American Mathematical Society*, vol. 127, no. 5, pp. 1427-1435.

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TY - JOUR

T1 - The holomorphic extension of Hp-CR functions on tube submanifolds

AU - Boggess, Albert

PY - 1999

Y1 - 1999

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=22644452199&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=22644452199&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:22644452199

VL - 127

SP - 1427

EP - 1435

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 5

ER -