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A Note on Hardy-Orlicz Spaces

Published online by Cambridge University Press:  20 November 2018

Zhang Jianzhong
Zhang Jianzhong*
Affiliation:
Department of Mathematics, Shaanxi Teachers University, Xi' an, China
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Abstract

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W. Deeb, R. Khalil and M. Marzuq have studied some properties of H(ϕ), the Hardy-Orlicz spaces. They introduced the functions class Np (0 < p ≦ 1 ) and discussed some properties of Np. In the present short note we prove that Np = N+ for 0 < p ≦ 1. We also give a condition of H(ϕ) = H(ψ).

Keywords

46A0646E20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 1 , 01 March 1990 , pp. 29 - 33
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Deeb, W., Khalil, R. and Marzuq, M., Isometric multiplication of Hardy-Orlicz spaces, Bull. Austral. Math. Soc. 34 (1986), 177–189.Google Scholar
2. Deeb, W. and Marzuq, M., H(ϕ) spaces, Canad. Math. Bull. 29(3) (1986), 295–301.Google Scholar
3. Duren, P. L., Theory of Hp spaces, Acad. Press, New York and London (1970).Google Scholar
4. Garnett, J. B., Bounded Analytic Functions, Acad. Press, New York (1981).Google Scholar