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Functions in All Hp Spaces, p < ∞

Published online by Cambridge University Press:  20 November 2018

Douglas M. Campbell
Douglas M. Campbell*
Affiliation:
Brigham Young University, Provo, Utah, 84602
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Abstract

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Let Ĥ denote the class of functions analytic in |z| < 1 which are in every Hp class, 0 < p < ∞. The class Ĥ strictly contains H∞ and consists of those functions that are ‘almost in H∞’ in the sense of integration. L. Hansen and W. Hayman have given simple geometric conditions for a function to belong to Ĥ. The purpose of this note is to show that Hansen and Hayman's conditions are far from necessary. Using techniques from normal functions, gap series, characterizations of BMOA, subordination, Bloch functions, and VMOA, six completely different examples of functions in Ĥ are given which ‘fill the plane’.

Keywords

30D4530C4530B10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 1 , 01 March 1982 , pp. 110 - 113
Copyright
Copyright © Canadian Mathematical Society 1982

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