A Note on Multipliers of Weighted Lebesgue Spaces

Birsen Sagir, Cenap Duyar

Abstract

In this paper, it is solved that the spaces $M\left( L_{w}^{p^{/}}\left(G\right) ,L_{w^{/}}^{\infty }\left( G\right) \right)$ and $L_{w}^{P}\left(G\right)$ can be topologically and algebraically identified, where $1\leqp^{/}<\infty, \frac{1}{p}+\frac{1}{p^{/}}=1$ and $w$ a Beurling weight ona locally compact Abelian group $G$. Also it is proved that the spaces $M\left( L_{w}^{1}\cap L_{w}^{p}\left( G\right), L_{w}^{1}\left( G\right)\right)$ can be identified with the weighted spaces of bounded measures $M_{w}\left( G\right)$.