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A pointwise growth estimate for analytic functions in tubes

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  • Richard D. Carmichael
  • Elmer K. Hayashi

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 .

Suggested Citation

  • Richard D. Carmichael & Elmer K. Hayashi, 1980. "A pointwise growth estimate for analytic functions in tubes," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 3, pages 1-7, January.
    • Handle: RePEc:hin:jijmms:513490
    DOI: 10.1155/S0161171280000439
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