A characterization of some weighted norm inequalities for maximal operators

摘要

It is found class of pairs of exponents (p(?), q(?)) such that for pairs of Banach function spaces (L~p(?)(?~n), L~q(?)(?~n)) weak Minkowski's inequality holds. Also some conditions which ensure the boundednness of maximal operator M': L~p(?)(?~n) → L~q(?)w (?~n) are found, when for the pair of Banach function spaces (L~p(?)(?~n), L~q(?) (?~n)) holds weak Minkowski's inequality.