Yves Rakotondratsimba

Abstract
A characterization is found  for multi-dimensional Hardy operators to be bounded from the weighted Lebesgue space $L^p(]0,\infty[^n, v(y_1,...\,,y_n) dy_1...\, dy_n)$ into $L^q(]0,\allowbreak\infty[^n, u(x_1,...\,,x_n) dx_1...\, dx_n)$ provided the weight $v^{1-p'}$ satisfies some doubling and reverse doubling conditions and where $1<p\le q<\infty$, $p'= p/(p-1)$.