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Hp multipliers and inequalities of Hardy and Littlewood

Published online by Cambridge University Press:  09 April 2009

G. I. Gaudry
G. I. Gaudry
Affiliation:
Mathematics Institute University of WarwickCoventry
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Consider the classical Hardy spaces Hp(T) (1 ≦ p ≦ ∞) on the unit circle T. We shall ignore completely the fact that the elements of Hp(T) can be extended via the Poisson formula to certain types of functions analytic inside the unit disc. For our purposes, Hp(T) is the closed ideal in Lp(T) consisting of those functions f ∈ Lp(T) for which (n) = 0 (n= –1, –2,…).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 10 , Issue 1-2 , August 1969 , pp. 23 - 32
Copyright
Copyright © Australian Mathematical Society 1969

References

[1]Edwards, R. E., Fourier series: a modern introduction, Vols I, II. (Holt, Rinehart and Winston, New York, 1967).Google Scholar
[2]Hoffman, Kenneth, Banach spaces of analytic functions, (Prentice-Hall, Englewood Cliffs 1962).Google Scholar
[3]Meyer, Yves, ‘Multiplicateurs des coefficients de Fourier des fonctions intégrables analytiques’, C. R. Acad. Sci. Paris, Sér. A—B, 263 (1966), A385–A387.Google Scholar
[4]Rudin, Walter, Fourier analysis on groups, (Interscience, New York 1962).Google Scholar
[5]Rudin, Walter, ‘Remarks on a theorem of Paley’, J. London Math. Soc., 32 (1957), 307–311.CrossRefGoogle Scholar
[6]Rudin, Walter, ‘Trigonometric series with gaps’, J. Math. and Mech., 9 (1960), 203–228.Google Scholar
[7]Zygmund, Antoni, Trigonometric series, Vol. II, (Cambridge University Press 1959).Google Scholar