Holomorphic extension of generalizations of H p functions

Richard D. Carmichael

International Journal of Mathematics and Mathematical Sciences, 1985, vol. 8, 1-8

Abstract:

In recent analysis we have defined and studied holomorphic functions in tubes in â„‚ n which generalize the Hardy H p functions in tubes. In this paper we consider functions f ( z ) , z = x + i y , which are holomorphic in the tube T C = â„ n + i C , where C is the finite union of open convex cones C j , j = 1 , … , m , and which satisfy the norm growth of our new functions. We prove a holomorphic extension theorem in which f ( z ) , z  ϵ  T C , is shown to be extendable to a function which is holomorphic in T 0 ( C ) = â„ n + i 0 ( C ) , where 0 ( C ) is the convex hull of C , if the distributional boundary values in 𝒮 ′ of f ( z ) from each connected component T C j of T C are equal.

Date: 1985
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:710426

DOI: 10.1155/S016117128500045X

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