On Weighted Norm Inequalities with Three Weights

Abstract

A characterization is given of the weights r, p, v when the weighted norm inequality ( ∫ a b | r f | q ) 1 / q ⩽ C ( ∫ a b | p f ′ | q + ∫ a b | v f | p ) 1 / p holds. Both cases 1 ⩽ p ⩽ q ⩽ ∞ and 1 ⩽ q < p ⩽ ∞ are considered and the related problems of compactness are also studied.