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

2010/07/19 by James Scurry, Scurry, James
Mathematics · #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Holomorphic and Operator Theory #Nonlinear Partial Differential Equations #math.CA

paper · pdf · doi:10.48550/arxiv.1007.3089

19 pages

openalex publication_date 2010/07/19 · arxiv created 2013/04/01 · arxiv updated 2013/04/02 · openalex created_date 2022/09/10 · openalex updated_date 2026/07/28

Abstract

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 < ∞. We are unaware of instances where this operator has been given attention in the two-weight setting before.

Citations

• Two Weight Inequalities for Discrete Positive Operators

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