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International Journal of Mathematics and Mathematical Sciences
Volume 2003, Issue 55, Pages 3503-3517
http://dx.doi.org/10.1155/S0161171203212205

Compactness in Wiener amalgams on locally compact groups

Department of Mathematics, Rani Durgawati University, Jabalpur, India

Received 18 December 2002

Copyright © 2003 Hindawi Publishing Corporation. 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

We study the compactness of bounded subsets in a Wiener amalgam whose local and global components are solid Banach function (BF) spaces on a locally compact group. Our main theorem provides a generalization of the corresponding results of Feichtinger. This paper paves the way for the study of compact multiplier operators on general Wiener amalgams on the lines of Feichtinger.