International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 3, Pages 575-581
A pointwise growth estimate for analytic functions in tubes
Department of Mathematics, Wake Forest University, Winston-Salem 27109, North Carolina, USA
Received 4 October 1979
Copyright © 1980 Richard D. Carmichael and Elmer K. Hayashi. 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.
A class of analytic functions in tube domains in -dimensional complex space, where is an open connected cone in , which has been defined by V. S. Vladimirov is studied. We show that a previously obtained growth estimate concerning these functions can be replaced by a pointwise growth estimate, and we obtain further new properties of these functions. Our analysis shows that these functions of Vladimirov are exactly the Hardy class of functions corresponding to the tube .