Structure m-convexe dans l'espace à poids $L_\Omega ^p\left( R^n\right) $

Abstract

We consider the space {\bf $L_\Omega ^p\left( R^n\right) ,$ }$1\leq p < +\infty ,$ where $\Omega $ is a family of weights. We give a necessary and sufficient condition, on $\Omega ,$ for {\bf $L_\Omega ^p\left( R^n\right) $ } to be locally m-convex algebra. Fundamental properties of this algebra are also obtained.