ArticleOriginal scientific text

Title

The holomorphic extension of Ck CR functions on tube submanifolds

Authors 1

Affiliations

  1. Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368, U.S.A.

Abstract

We show that a CR function of class Ck, 0 ≤ k < ∞, on a tube submanifold of 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 Ck-norm of the extension is shown to be no bigger than the Ck-norm of the original CR function.

Keywords

CR function, convex, tube

Bibliography

  1. [BD] A. Boivin and R. Dwilewicz, Extension and approximation of CR functions on tube manifolds, Trans. Amer. Math. Soc. 350 (1998), 1945-1956.
  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.
  3. [SW] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, 1971.
Pages:
35-42
Main language of publication
English
Received
1997-12-18
Accepted
1998-08-17
Published
1998
Exact and natural sciences