A note on two-weight inequalities for multiple Hardy-type operators (Q2574410)

The author provides boundedness criteria for the Riemann--Liouville operator \[ R_{\alpha,\beta} f(x,y)= \int^x_0 \int^y_0 {f(t,\tau)\over (x- t)^{1-\alpha}(y- \tau)^{1-\beta}}\,dt\,d\tau\quad (\alpha,\beta> 1) \] from \(L^p_w(\mathbb{R}^2_+)\) to \(L^q_v(\mathbb{R}^2_+)\), where \(1< p\leq q<\infty\) and \(w\), \(v\) are certain weights (\(w\) satisfies the one-dimensional doubling condition uniformly with respect to another variable).