Fourier transforms of Dini-Lipschitz functions. (1986) - Younis, M. S.
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.