A pointwise growth estimate for analytic functions in tubes

Richard D. Carmichael and Elmer K. Hayashi

International Journal of Mathematics and Mathematical Sciences, 1980, vol. 3, 1-7

Abstract:

A class of analytic functions in tube domains T C = â„ n + i C in n -dimensional complex space, where C is an open connected cone in â„ n , which has been defined by V. S. Vladimirov is studied. We show that a previously obtained L 2 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 H 2 class of functions corresponding to the tube T C .

Date: 1980
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:513490

DOI: 10.1155/S0161171280000439

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