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A Density problem for Hardy spaces of almost periodic functions

Published online by Cambridge University Press:  17 April 2009

Robyn Owens
Robyn Owens
Affiliation:
Department of Mathematics, University of Western Australia, Nedlands, Western Australia 6009, Australia.
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Abstract

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We construct a counterexample, for p = 1, to the conjecture posed by Milaszevitch in 1970: is the space of functions which are analytic in the upper half plane and uniformly almost periodic in its closure dense in the Hardy space Hp (0 < p ∞) of analytic almost periodic functions?

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 29 , Issue 3 , June 1984 , pp. 315 - 327
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Garnett, J., Bounded analytic functions (Academic Press, New York and London, 1980).Google Scholar
[2]Hoffman, K., “Boundary behaviour of generalized analytic functions”, Trans. Amer. Math. Soc. 87 (1958), 447–466.CrossRefGoogle Scholar
[3]Holland, F., “Harmonic analysis on amalgams of Lp and lq”, J. London Math. Soc. (2) 10 (1975), 295–305.CrossRefGoogle Scholar
[4]Milaszevitch, J., “Hardy spaces of almost periodic functions”, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 24 (1970), 401–428.Google Scholar
[5]Owens, R., “A maximal function characterization of a class of Hardy spaces”, submitted.Google Scholar
[6]Zygmund, A., Trigonometrical series, 2nd edition (Cambridge University Press, Cambridge, 1959).Google Scholar