Weighted inequalities for multi-dimensional Hardy operators. (Q1862727)

Let \(1<p\leq q<\infty\). In this paper the author characterizes the couples \((u, v)\) of weights on \((0, \infty)^n\) such that the \(n\)-dimensional Hardy operator \[ (H_nf)(x_1,\dots,x_n)=\int_0^{x_1}\dots\int_0^{x_n} f(y_1,\dots,y_n)\,dy_1\cdots dy_n \] is bounded from \(L^p(v)\) to \(L^q(u)\), under some doubling conditions over \(v^{1-p}\), with \(p=p/(p-1)\).