Fourier transforms of Dini-Lipschitz functions. (1986)

• Record Type: Journal Article
• Authors: Younis, M. S.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 9:Number 2(1986)
• Page Start: 301
• Page End: 312
• Publication Date: 1986
• Subjects: Dini-Lipschitz functions -- Fourier series -- Fourier transforms; Mathematics -- Periodicals; 510.5
• DOI: 10.1155/S0161171286000376
• Languages: English
• ISSNs: 0161-1712

Abstract

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.