Complex-Tangential Sets and Boundary Values in Submanifolds of the Boundary.

A. Noell; W.C. Ramey; D.C. Ullrich

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We prove that continuity properties of bounded analytic functions in bounded smoothly bounded pseudoconvex domains in two-dimensional affine space are determined by their behaviour near the Shilov boundary. Namely, if the function has continuous extension to an open subset of the boundary containing the Shilov boundary it extends continuously to the whole boundary. If it is Hölder continuous on such a boundary set, it is Hölder continuous on the closure of the domain. The statements...