Two weight norm inequality for the fractional maximal operator and the fractional integral operator

Abstract

New su±cient conditions on the weight functions u(:) and v(:) are given in order that the fractional maximal [resp. integral] operator Ms [resp. Is], 0 · s < n, [resp. 0 < s < n] sends the weighted Lebesgue space Lp(v(x) dx) into Lp(u(x)dx), 1 < p < 1. As a consequence a characterization for this estimate is obtained whenever the weight functions are radial monotone