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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 986857, 12 pages
http://dx.doi.org/10.1155/2013/986857
Research Article

Some Intersections of the Weighted -Spaces

Department of Mathematics, University of Isfahan, Isfahan 81746-73441, Iran

Received 24 March 2013; Revised 25 May 2013; Accepted 27 August 2013

Academic Editor: Sung Guen Kim

Copyright © 2013 F. Abtahi 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.

Abstract

Let be a locally compact group an arbitrary family of the weight functions on and . The locally convex space as a subspace of is defined. Also, some sufficient conditions for that space to be a Banach space are provided. Furthermore, for an arbitrary subset of and a positive submultiplicative weight function on , Banach subspace of is introduced. Then some algebraic properties of , as a Banach algebra under convolution product, are investigated.