Weighted one-dimensional Poincaré inequalities in Banach function spaces

Abstract

We characterize some weighted one-dimensional Poincaré inequalities on Banach function spaces, generalizing in this way Chua and Wheeden’s theorem in the case p q. As particular cases, we get the characterizations of some weighted Orlicz- Poincaré inequalities and Poincaré inequalities in variable Lebesgue spaces. We also get a new result on weighted weak-type inequalities of this kind.