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The holomorphic extension of C k CR functions on tube submanifolds

Al Boggess (1998)

Annales Polonici Mathematici

We show that a CR function of class C k , 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 C k -norm of the extension is shown to be no bigger than the C k -norm of the original CR function.

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