The two-weight inequality for the Hilbert transform with general measures

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Hytönen , T P 2018 , ' The two-weight inequality for the Hilbert transform with general measures ' , Proceedings of the London Mathematical Society , vol. 117 , no. 3 , pp. 483–526 . https://doi.org/10.1112/plms.12136

Title: The two-weight inequality for the Hilbert transform with general measures
Author: Hytönen, Tuomas P.
Contributor: University of Helsinki, Tuomas Hytönen / Principal Investigator
Date: 2018-09
Language: eng
Number of pages: 44
Belongs to series: Proceedings of the London Mathematical Society
ISSN: 0024-6115
URI: http://hdl.handle.net/10138/307044
Abstract: The two‐weight inequality for the Hilbert transform is characterized for an arbitrary pair of positive Radon measures σ and w on ℝ. In particular, the possibility of common point masses is allowed, lifting a restriction from the recent solution of the two‐weight problem by Lacey, Sawyer, Shen, and Uriarte‐Tuero. Our characterization is in terms of Sawyer‐type testing conditions and a variant of the two‐weight A2 condition, where σ and w are integrated over complementary intervals only. A key novelty of the proof is a two‐weight inequality for the Poisson integral with ‘holes’.
Subject: 111 Mathematics
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