International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 3, Pages 435-443
doi:10.1155/S0161171281000306
Growth of HP functions in tubes
Department of Mathematics, Wake Forest University, Winston-Salem 27109, North Carolina, USA
Received 9 October 1980
Copyright © 1981 Richard D. Carmichael and Stephen P. Richters. 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.
Abstract
Let C be an open convex cone in n dimensional real space Rn such that C¯ does not contain any entire straight line. We obtain a growth condition on functions in the Hardy spaces HP(TC), 1≤p≤∞, corresponding to the tube TC=Rn+iC in n dimensional complex space ℂn.