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

In this paper, we define $A_{\vartheta {1},\vartheta {2}}^{p,1,q,r}\left(G\right) $tobespaceofallfunctionsin$\left( L{\vartheta{1}}^{p},\ell ^{1}\right) $whoseFouriertransformsbelongto$\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.