We prove that for any weight ϕ defined on [0,1]n that satisfies a reverse Holder inequality with exponent p > 1 and constant c≥1 upon all dyadic subcubes of [0,1]n, it's non increasing rearrangement satisfies a reverse Holder inequality with the same exponent and constant not more than 2nc−2n+1, upon all subintervals of [0;1] of the form [0;t]. This gives as a consequence, according to the results in [8], an interval [p;p0(p;c))=Ip,c, such that for any q∈Ip,c, we have that ϕ is in Lq.
