Multiplication operators on amalgam of $l^{q), \theta}$ and $L^{p}$

Abstract

We define the grand amalgam Lebesgue function space $l^{q), \theta}(L^p),$ and study the fundamental structural properties of the space, including completeness. Then we define the small Lebesgue sequence space and study its function space properties. Furthermore, we prove a version of the H\"{o}lders inequality on the frame work of these spaces. Finally, we study the multiplication operator in the setting of these spaces.