### Abstract

We consider the space, CR^{p}(M), consisting of CR functions which also lie in L^{p}(M) on a quadric submanifold M of C^{n} of codimension at least one. For 1 ≤ p ≤ ∞, we prove that each element in CR^{p}(M) extends uniquely to an H^{p} function on the interior of the convex hull of M. As part of the proof, we establish a semi-global version of the CR approximation theorem of Baouendi and Treves for submanifolds which are graphs and whose graphing functions have polynomial growth.

Original language | English (US) |
---|---|

Pages (from-to) | 1-18 |

Number of pages | 18 |

Journal | Pacific Journal of Mathematics |

Volume | 201 |

Issue number | 1 |

State | Published - Nov 2001 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**CR extension for L ^{p} CR functions on a quadric submanifold of C^{n}
.** / Boggess, Albert.

Research output: Contribution to journal › Article

^{p}CR functions on a quadric submanifold of C

^{n}',

*Pacific Journal of Mathematics*, vol. 201, no. 1, pp. 1-18.

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TY - JOUR

T1 - CR extension for Lp CR functions on a quadric submanifold of Cn

AU - Boggess, Albert

PY - 2001/11

Y1 - 2001/11

N2 - We consider the space, CRp(M), consisting of CR functions which also lie in Lp(M) on a quadric submanifold M of Cn of codimension at least one. For 1 ≤ p ≤ ∞, we prove that each element in CRp(M) extends uniquely to an Hp function on the interior of the convex hull of M. As part of the proof, we establish a semi-global version of the CR approximation theorem of Baouendi and Treves for submanifolds which are graphs and whose graphing functions have polynomial growth.

AB - We consider the space, CRp(M), consisting of CR functions which also lie in Lp(M) on a quadric submanifold M of Cn of codimension at least one. For 1 ≤ p ≤ ∞, we prove that each element in CRp(M) extends uniquely to an Hp function on the interior of the convex hull of M. As part of the proof, we establish a semi-global version of the CR approximation theorem of Baouendi and Treves for submanifolds which are graphs and whose graphing functions have polynomial growth.

UR - http://www.scopus.com/inward/record.url?scp=0039894268&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039894268&partnerID=8YFLogxK

M3 - Article

VL - 201

SP - 1

EP - 18

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 1

ER -