Michael T. Lacey
Published 2013-04-18, updated 2015-09-06Version 4
Recent work of Lacey-Sawyer-Shen-Uriarte-Tuero and Lacey have established a conjecture of Nazarov-Treil-Volberg, giving a real-variable characterization of the two weight inequality for the Hilbert transform, provided the pair of weights do not share a common point mass. In this paper, the characterization is proved, collecting details from across several papers, compactness is characterized, all relevant estimates are proved, counterexamples are details, and areas of application are indicated.
Comments: 77 pages, 10 figures. Global to Local done in a direct fashion. To appear in the Cora Sadosky memorial volume
The Two Weight Inequality for Hilbert Transform, Coronas, and Energy Conditions
A new characterization of Sobolev spaces on $\mathbb{R}^n$
Notes on the characterization of derivations
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