Dyadic weights on R-n and reverse Holder inequalities

摘要

We prove that for any weight phi defined on [0; 1](n) that satisfies a reverse Holder inequality with exponent p > 1 and constant c >= 1 on all dyadic subcubes of [0; 1](n), its non-increasing rearrangement phi* satisfies a reverse Holder inequality with the same exponent and constant not more than 2(n)c - 2(n) + 1 on all subintervals of the form [0; t], 0 < t <= 1. As a consequence, there is an interval [p; p(0) (p; c)) = I-p,I-c such that phi is an element of L-q for any q is an element of I-p,I-c.