# The holomorphic extension of ${C}^{k}$ CR functions on tube submanifolds

Annales Polonici Mathematici (1998)

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

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topAl 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

top- [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
- [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
- [SW] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, 1971.

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