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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

Information

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

References

1. Duren, P. L., Romberg, B. W. and Shields, A. L., Linear functional s on Hp spaces with 0 < p < 1, J. Reine Angew. Math. 238 (1969), pp. 32–60.Google Scholar
2. Duren, P. L., Theory of Hp Spaces, Pure and Appl. Math., no. 38, Academic Press, New York and London (1970).Google Scholar
3. Hahn, K. T. and Mitchell, J., Hp spaces on bounded symmetric domains, Trans. Amer. Math. Soc, 146 (1969), pp. 521–531.Google Scholar
4. Rudin, W., Functional Analysis, McGraw-Hill, New York (1973).Google Scholar
5. Walters, S., Remarks on the space Hp, Pacific J. Math. 1 (1951), pp. 455–471.Google Scholar
6. Yanagihara, N., Multipliers and linear functionals for the class N+ , Trans. Amer. Math. Soc, 180 (1973), pp. 449–461.Google Scholar