International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 1, Pages 57-66

On a family of Wiener type spaces

R. H. Fischer,1,2 A. T. Gürkanli,1,2 and T. S. Liu1,2

1University of Massachusetts, Department of Mathematics and Statistic, Amherst 01003, MA., USA
2Ondokuz Mayis University, Faculty of Art and Sciences, Department of Mathematics, Samsun, Turkey

Received 16 June 1993; Revised 20 June 1994

Copyright © 1996 R. H. Fischer et al. 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.


Research on Wiener type spaces was initiated by N.Wiener in [15]. A number of authors worked on these spaces or some special cases of these spaces. A kind of generalization of the Wiener's definition was given by H.Feichtinger in [2] as a Banach spaces of functions (or measures, distributions) on locally compact groups that are defined by means of the global behaviour of certain local properties of their elements. In the present paper we discussed Wiener type spaces using the spaces Aw,ωp,q(G) and Fw,ωp,q(G) (c. f. [8]) as a local component, and Lνr(G) as a global component, where w and ν are Beurling weights on G and ω is a Beurling weight on Gˆ (c. f. [13]).