International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 2, Pages 301-312

Fourier transforms of Dini-Lipschitz functions

M. S. Younis

Department of Mathematics, Yarmouk University, Irbid, Jordan

Received 29 October 1984

Copyright © 1986 M. S. Younis. 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.


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.