The Banach Algebra of Functions With Fourier Transforms in Weighted Amalgam Spaces

Abstract

In this paper, we define $A_{{\vartheta }_1,{\vartheta }_2}^{p,1,q,r}\left(G\right)$ to be space of all functions in $\left(L_{{\vartheta }_1}^p,{\ell }^1\right)$ whose Fourier transforms belong to $\left(L_{{\vartheta }_2}^q,{\ell }^r\right).$ Moreover, we consider the basic and advance properties of this space including Banach algebra, translation invariant, Banach module, a generalized type of Segal algebra etc. Also, we study some inclusions, compact embeddings in sense to weights and further discuss multipliers of this space.

15 Pages