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 Hölders inequality on the frame work of these spaces. Finally, we study the multiplication operator in the setting of these spaces.

20 pages