The holomorphic extension of $C^k$ CR functions on tube submanifolds
Volume 70 / 1998
Annales Polonici Mathematici 70 (1998), 35-42 DOI: 10.4064/ap-70-1-35-42
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.