Morera Theorems for the Boundary Values of Holomorphic Functions in the Unit Ball in C

Content Provider	Semantic Scholar
Author	Govekar-Leban, Darja
Copyright Year	2007
Abstract	Let , , be the open unit ball. From Theorem 2.4 in [BCPZ] (for Theorem 2.4 in [BCPZ] is a result of Globevnik and Stout [GS]) it follows that there exists a non-empty and at most countable set such that if and then the Morera property of with respect to all affine complex hyperplanes at a distance from the origin is sufficient to guarantee that extends through as a member of the algebra of functions continuous on and holomorphic on . Moreover, if then there exists a function which does not continue to a function from the ball algebra but satisfies the Morera condition with respect to every affine complex hyperplane at a distance from the origin. In this paper we prove that the analogous statement holds if we replace the Morera conditions along complex hyperplanes at a fixed distance from the origin with the in some sense weaker Morera conditions along real hyperplanes at a fixed distance from the origin, that is, if we replace the integral conditions over certain submanifolds of of real codimension with the integral conditions over certain submanifolds of of minimal real codimension .
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Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article