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H(ϕ) Spaces

Published online by Cambridge University Press:  20 November 2018

W. Deeb  and
M. Marzuq
W. Deeb
Affiliation:
Department of Mathematics, Kuwait University, Kuwait
M. Marzuq
Affiliation:
Department of Mathematics, Kuwait University, Kuwait
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Abstract

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Let ψ be a non-decreasing continuous subadditive function defined on [0, ∞) and satisfy ψ(x) = 0 if and only if x = 0. The space H(ψ) is defined as the set of analytic functions in the unit disk which satisfy

and the space H+ (ψ) is the space of a f ∊ H(ψ) for which

where almost everywhere.

In this paper we study the H(ψ) spaces and characterize the continuous linear functionals on H+ (ψ).

Keywords

46A0646E1030H05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 3 , 01 September 1986 , pp. 295 - 301
Copyright
Copyright © Canadian Mathematical Society 1986

References

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