International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 3, Pages 435-443

Growth of HP functions in tubes

Richard D. Carmichael and Stephen P. Richters

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.


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), 1p, corresponding to the tube TC=Rn+iC in n dimensional complex space n.