A Characterization of a Two-Weight Inequality for Discrete Two-Dimensional Hardy Operators

Abstract

We obtain a characterization of non-negative double sequences $V=V(n_1,n_2){)}_{n_1,n_2}$ and $U=(U(n_1,n_2){)}_{n_1,n_2}$ for which the two-dimensional discrete Hardy operator $\mathbb{H}$ is bounded from $l^p(V)$ into $l^q(U)$ whenever $1<p\le q<\infty$.