Sharp L p -weighted Sobolev inequalities

Abstract

We prove sharp weighted inequalities of the form ∫ R n | f ( x ) | p v ( x ) d x ≤ C ∫ R n | q ( D ) ( f ) ( x ) | p N ( v ) ( x ) d x where q ( D ) is a differential operator and N is a combination of maximal type operator related to q ( D ) and to p .