A Characterization of Two-Weight Inequalities for a Vector-Valued Operator

Details A Characterization of Two-Weight Inequalities for a Vector-Valued Operator A Characterization of Two-Weight Inequalities for a Vector-Valued Operator

2010-07-19

arxiv.org/abs/1007.3089v1

Mathematics

Classical Analysis and ODEs

19 pages

Scientific paper

We give a characterization of the two-weight inequality for a simple vector-valued operator. Special cases of our result have been considered before in the form of the weighted Carleson embedding theorem, the dyadic positive operators of Nazarov, Treil, and Volberg in the square integrable case, and Lacey, Sawyer, Uriarte-Tuero in the L^p case. The main technique of this paper is a Sawyer-style argument and the characterization is for 1 < p < \infty. We are unaware of instances where this operator has been given attention in the two-weight setting before.

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