Fourier transforms of Dini-Lipschitz functions

Abstract

It is well known that if Lipschitz conditions of a certain order are imposed on a functionf(x), then these conditions affect considerably the absolute convergence of the Fourier series and Fourier transforms off. In general, iff(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 off(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.