The two-weight inequality for the Hilbert transform with general measures
Classical Analysis and ODEs
2019-11-19 v3 Functional Analysis
Abstract
The two-weight inequality for the Hilbert transform is characterized for an arbitrary pair of positive Radon measures and on . 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 condition, where and are integrated over complementary intervals only. A key novely of the proof is a two-weight inequality for the Poisson integral with `holes'.
Cite
@article{arxiv.1312.0843,
title = {The two-weight inequality for the Hilbert transform with general measures},
author = {Tuomas P. Hytönen},
journal= {arXiv preprint arXiv:1312.0843},
year = {2019}
}
Comments
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