Two weight inequalities for individual Haar multipliers and other well localized operators

By Fedor Nazarov, Sergei Treil, Alexander Volberg. 2007

102 citations recorded by the source corpus.

In this paper we are proving that Sawyer type condition for boundedness work for the two weight estimates of individual Haar multipliers, as well as for the Haar shift and other ``well localized'' operators.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/fc8895c31a12cf2d7d1eabaccbce5cd21c99026e

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In Applied Mathematics

Citations in the corpus

Commutators in the two-weight setting (2015, result): “For operators with a more singular nature we point to the work of Nazarov, Treil and Volberg in [33], Lacey, Sawyer, Shen, and Uriarte-Tuero in [24], Lacey in [20], Lacey, Sawyer, Shen, Uriarte-Tuero and Wick in [25] and Lacey and Wick”
The sharp weighted bound for general Calderón-Zygmund operators (2010, background): “on for dyadic cubes only, which would somewhat simplify the preceding analysis. Indeed, a result of this ﬂavour is provided by Nazarov–Treil–Volberg’s two-weight inequality for dyadic shift operators [20] (which lies behind Lacey–Petermichl–Reguera’s result [13]). But in order to apply it to the des”
A Two Weight Inequality for the Hilbert transform Assuming an Energy Hypothesis (2010, methodology): “ - see e.g. Theorem 2.1 in [NiTr]. The approach of Nazarov, Treil and Volberg involves a delicate combination of ideas: random grids (see [NTV2]), weighted Haar functions and Carleson embeddings (see [NTV3]), stopping intervals (see [Vol]) and culminates in the use of these techniques with a corona ”
Sharp weighted estimates for approximating dyadic operators (2010, methodology): “Their proof avoids the use of Bellman functions, and instead uses a deep, twoweight “Tb theorem” for Haar shift operators due to Nazarov, Treil and Volberg [16].”
A characterization of two weight norm inequalities for maximal singular integrals with one doubling measure (2008, methodology): “transform, but with the additional assumption that ˙is doubling for the strong type inequality. A major point of our characterizations is that they hold for all 1 <p<1. The methods in [4], [8], [9], [10], [11] apply only to the case p= 2, where the orthogonality of measure-adapted Haar bases p”
Sharp weighted norm estimates beyond Calderón–Zygmund theory (2015, unknown): “While [Nazarov et al. 1999] inﬂuenced earlier proofs, [Nazarov et al. 2008] was important for later proofs.”
Sharp weighted norm inequalities for Littlewood-Paley operators and singular integrals (2010, methodology): “Recently, Lacey, Petermichl and Reguera [11] have established sharp weighted estimates for Haar shift operators without the use of Bellman functions; their proof uses a two-weight “Tb theorem” for Haar shift operators due to Nazarov, Treil and Volberg [15].”
Two weight norm inequalities for fractional integral operators and commutators (2014, methodology): “[101] A. Volberg.”
Weighted martingale multipliers in non-homogeneous setting and outer measure spaces (2014, background): “1 below (for homogeneous situation such result for well localized operators was proved in [11]), the inequality (4.”
Representation of singular integrals by dyadic operators, and the A_2 theorem (2011, result): “[14] Fedor Nazarov, Alexander Reznikov, and Alexander Volberg.”