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 organization: | Tuomas Hytönen / Principal Investigator Department of Mathematics and Statistics |
| Date: | 2018-09 |
| Language: | eng |
| Number of pages: | 44 |
| Belongs to series: | Proceedings of the London Mathematical Society |
| ISSN: | 0024-6115 |
| DOI: | https://doi.org/10.1112/plms.12136 |
| 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 |
| Peer reviewed: | Yes |
| Usage restriction: | openAccess |
| Self-archived version: | acceptedVersion |
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