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International Journal of Mathematics and Mathematical Sciences
Volume 3, Issue 3, Pages 575-581

A pointwise growth estimate for analytic functions in tubes

Department of Mathematics, Wake Forest University, Winston-Salem, North Carolina 27109, USA

Received 4 October 1979

Copyright © 1980 Hindawi Publishing Corporation. 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 TC=n+iC in n-dimensional complex space, where C is an open connected cone in n, which has been defined by V. S. Vladimirov is studied. We show that a previously obtained L2 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 H2 class of functions corresponding to the tube TC.