On two weight estimates for dyadic operators

2016/02/05 by Oleksandra Beznosova, Daewon Chung, Beznosova, Oleksandra +5
Mathematics · #Advanced Harmonic Analysis Research #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1602.02084

Abstract

We provide a quantitative two weight estimate for the dyadic paraproduct π_b under certain conditions on a pair of weights (u;v) and b in Carl_u,v, a new class of functions that we show coincides with BMO when u = v ∈ A^d₂. We obtain quantitative two weight estimates for the dyadic square function and the martingale transforms under the assumption that the maximal function is bounded from L₂(u) into L₂(v) and v ∈ RH^d₁. Finally we obtain a quantitative two weight estimate from L₂(u) into L₂(v) for the dyadic square function under the assumption that the pair (u; v) is in joint A^d₂ and u^-1 ∈ RH^d₁, this is sharp in the sense that when u = v the conditions reduce to u ∈ A^d₂ and the estimate is the known linear mixed estimate.

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