International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 3, Pages 417-424

Holomorphic extension of generalizations of Hp functions

Richard D. Carmichael

Department of Mathematical Sciences, New Mexico State University, Las Cruces 88003, New Mexico, USA

Received 31 March 1985

Copyright © 1985 Richard D. Carmichael. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In recent analysis we have defined and studied holomorphic functions in tubes in n which generalize the Hardy Hp functions in tubes. In this paper we consider functions f(z), z=x+iy, which are holomorphic in the tube TC=n+iC, where C is the finite union of open convex cones Cj, 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 TC, is shown to be extendable to a function which is holomorphic in T0(C)=n+i0(C), where 0(C) is the convex hull of C, if the distributional boundary values in 𝒮 of f(z) from each connected component TCj of TC are equal.