The holomorphic extension of C k CR functions on tube submanifolds

Al Boggess

Annales Polonici Mathematici (1998)

  • Volume: 70, Issue: 1, page 35-42
  • ISSN: 0066-2216

Abstract

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We show that a CR function of class C k , 0 ≤ k < ∞, on a tube submanifold of ℂ n holomorphically extends to the convex hull of the submanifold. The extension and all its derivatives through order k are shown to have nontangential pointwise boundary values on the original tube submanifold. The C k -norm of the extension is shown to be no bigger than the C k -norm of the original CR function.

How to cite

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Al Boggess. "The holomorphic extension of $C^k$ CR functions on tube submanifolds." Annales Polonici Mathematici 70.1 (1998): 35-42. <http://eudml.org/doc/262550>.

@article{AlBoggess1998,
abstract = {We show that a CR function of class $C^k$, 0 ≤ k < ∞, on a tube submanifold of $ℂ^n$ holomorphically extends to the convex hull of the submanifold. The extension and all its derivatives through order k are shown to have nontangential pointwise boundary values on the original tube submanifold. The $C^k$-norm of the extension is shown to be no bigger than the $C^k$-norm of the original CR function.},
author = {Al Boggess},
journal = {Annales Polonici Mathematici},
keywords = {CR function; convex; tube; tube manifold; analytic disc},
language = {eng},
number = {1},
pages = {35-42},
title = {The holomorphic extension of $C^k$ CR functions on tube submanifolds},
url = {http://eudml.org/doc/262550},
volume = {70},
year = {1998},
}

TY - JOUR
AU - Al Boggess
TI - The holomorphic extension of $C^k$ CR functions on tube submanifolds
JO - Annales Polonici Mathematici
PY - 1998
VL - 70
IS - 1
SP - 35
EP - 42
AB - We show that a CR function of class $C^k$, 0 ≤ k < ∞, on a tube submanifold of $ℂ^n$ holomorphically extends to the convex hull of the submanifold. The extension and all its derivatives through order k are shown to have nontangential pointwise boundary values on the original tube submanifold. The $C^k$-norm of the extension is shown to be no bigger than the $C^k$-norm of the original CR function.
LA - eng
KW - CR function; convex; tube; tube manifold; analytic disc
UR - http://eudml.org/doc/262550
ER -

References

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  1. [BD] A. Boivin and R. Dwilewicz, Extension and approximation of CR functions on tube manifolds, Trans. Amer. Math. Soc. 350 (1998), 1945-1956. Zbl0903.32005
  2. [BT] M. S. Baouendi and F. Treves, A property of the functions and distributions annihilated by a locally integrable system of complex vector fields, Ann. of Math. 113 (1981), 387-421. Zbl0491.35036
  3. [SW] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, 1971. 

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