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On the moduli of continuity of Hp functions with 0<p<1

Published online by Cambridge University Press:  20 January 2009

Miroslav Pavlović
Miroslav Pavlović
Affiliation:
Matematički FakultetStudentski Trg 1611000 Beograd, Yugoslavia
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We prove two inequalities which relate the Lp modulus of continuity of n-th order, ωn(f,·)p, of an Hp function f with the p-th mean values of the n-th derivative f(n). Using these inequalities we extend classical results of Hardy and Littlewood [5], Gwiliam [4], Zygmund [13] and Taibleson [12] as well as a recent result of Oswald [6].

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 35 , Issue 1 , February 1992 , pp. 89 - 100
Copyright
Copyright © Edinburgh Mathematical Society 1992

References

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