On some compact embeddings of a weighted space

Abstract

In this paper, we define an intersection spaces between weighted classical Lebesgue spaces and an amalgam space with two weight functions on a locally compact abelian group with Haar measure. We consider the basic properties of the space such as Banach algebra, translation invariant, Banach module, a generalized type of Segal algebra etc. Also, we investigate some inclusions, compact embeddings in sense to weights and further discuss multipliers of this space.