Some Properties of Weighted Norm Inequalities for the Hardy-Littlewood Maxima Function

Abstract

Many researchers have expended their efforts on Hardy-Littlewood Maxima operator but little or no work has been done if the operator is acting on a power function. In this article, new characterization of Hardy-Littlewood Maxima operator bounded from Lp (Rn,wdx) to Lq (Rn,vdx) for weight functions v(x) and some non-trivial w(x) are proved. Our novel methods generalized and sharpened Wo-sang Young results to perfection.