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Generalized absolute continuity of a function of Wiener's class

Published online by Cambridge University Press:  17 April 2009

Rafat Nabi Siddiqi
Rafat Nabi Siddiqi
Affiliation:
Department of Mathematics, Kuwait University, Kuwait, Arabian Gulf.
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Abstract

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In the present paper we give a criterion for a function of Wiener's class to belong to the class of generalized absolute continuity, in terms of Fourier-Young coefficients {Ck}. More precisely, we prove the following theorem.

THEOREM. Let Λ = (λn,k) be a normal almost periodic matrix of real numbers such that λn,k ≥ λn,k+1 for all n and k. Then for any function f of Wiener's class Vν (1 < ν < 2) to be of class of generalized absolute continuity Ap (1 < p < ∞) it is necessary and sufficient that {|Ck|2} is summable Λ to zero.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 22 , Issue 2 , October 1980 , pp. 253 - 258
Copyright
Copyright © Australian Mathematical Society 1980

References

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