# A Characterization of Two-Weight Inequalities for a Vector-Valued Operator - Mathematics > Classical Analysis and ODEs

Abstract: We give a characterization of the two-weight inequality for a simplevector-valued operator. Special cases of our result have been considered beforein the form of the weighted Carleson embedding theorem, the dyadic positiveoperators of Nazarov, Treil, and Volberg in the square integrable case, andLacey, Sawyer, Uriarte-Tuero in the L^p case. The main technique of this paperis a Sawyer-style argument and the characterization is for 1 < p < \infty. Weare unaware of instances where this operator has been given attention in thetwo-weight setting before.

Author: James Scurry

Source: https://arxiv.org/