A Characterization of Some Weighted Norm Inequalities for Maximal Operators
Tengiz Kopaliani
Tbilisi State University, Georgia

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.
Cite this article
Tengiz Kopaliani, A Characterization of Some Weighted Norm Inequalities for Maximal Operators. Z. Anal. Anwend. 29 (2010), no. 4, pp. 401–412
DOI 10.4171/ZAA/1414