Compactness in Wiener amalgams on locally compact groups (Q1415200)

The concept of Wiener amalgams on a locally compact group was introduced by \textit{G. H. Feich\-tin\-ger} [Arch. Math. (Basel) 29, 136--140 (1977; Zbl 0363.43003)]. In a series of papers Feichtinger has explored the vital role of Wiener amalgams in general harmonic analysis and its various applications. These spaces, in fact, describe the global and local behaviours of functions or distributions independently and provide very convenient generalizations of the classical function and sequence spaces. In the paper under review the author defines the Wiener amalgam \(W(B,Y)({\mathcal G})\) in the case when \(\mathcal G\) is a locally compact group and the local and global components \(B\) and \(Y\) are both solid Banach function spaces and satisfy some other suitable conditions. The main theorem of the paper gives compactness conditions of bounded subsets of a general Wiener amalgam. This theorem provides a generalization of the corresponding results of Feichtinger.