A Characterization of Some Weighted Norm Inequalities for Maximal Operators

Abstract

It is found class of pairs of exponents (p(·), q(·)) such that for pairs of Banach function spaces (Lp(·)(ℝ_n_), Lq(·)(ℝ_n_)) weak Minkowski’s inequality holds. Also some conditions which ensure the boundednness of maximal operator M_φ: Lp(·)(ℝ_n) → Lq(·)w (ℝ_n_) are found, when for the pair of Banach function spaces (Lp(·)(ℝ_n_) , Lq(·)(ℝ_n_)) holds weak Minkowski’s inequality.