International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1986 / Article

Open Access

Volume 9 |Article ID 783650 | https://doi.org/10.1155/S0161171286000376

M. S. Younis, "Fourier transforms of Dini-Lipschitz functions", International Journal of Mathematics and Mathematical Sciences, vol. 9, Article ID 783650, 12 pages, 1986. https://doi.org/10.1155/S0161171286000376

Fourier transforms of Dini-Lipschitz functions

Received29 Oct 1984

Abstract

It is well known that if Lipschitz conditions of a certain order are imposed on a function f(x), then these conditions affect considerably the absolute convergence of the Fourier series and Fourier transforms of f. In general, if f(x) belongs to a certain function class, then the Lipschitz conditions have bearing as to the dual space to which the Fourier coefficients and transforms of f(x) belong. In the present work we do study the same phenomena for the wider Dini-Lipschitz class as well as for some other allied classes of functions.

Copyright © 1986 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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