Amalgam Spaces With Variable Exponent

Abstract

Let $1\leq s<\infty $ and $1\leq r(.)\leq \infty $ where $r(.)$ is a variable exponent. In this study, we consider the variable exponent amalgam space $\left( L^{r(.)},\ell ^{s}\right) $. Moreover, we present some examples about inclusion properties of this space. Finally, we obtain that the space $\left( L^{r(.)},\ell ^{s}\right) $ is a Banach Function space.