On a family of Wiener type spaces

Abstract

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 spacesAw,ωp,q(G)andFw,ωp,q(G)(c. f. [8]) as a local component, andLνr(G)as a global component, wherewandνare Beurling weights onGandωis a Beurling weight onGˆ(c. f. [13]).