New properties of grand amalgam spaces

Abstract

In $ \left[14\right]$, a new family called grand amalgam space $W( L^{p),\theta},L^{q),\theta })$ of amalgam spaces was defined and investigated properties of these spaces. The present paper is a sequel to my work $[14].$ In this paper, notations are included in Section 1. In Section 2, we introduce another equivalent but discrete definition of grand amalgam space and study properties of these spaces. In Section 3, we determine necessary and sufficient conditions on a locally compact Abelian group $G$ for the grand amalgam spaces $W(L^{p,)\theta},L^ {q,\theta})$ to be an algebra under convolution.