A two weight local Tb theorem for the Hilbert transform
Classical Analysis and ODEs
2019-06-24 v9
Abstract
We obtain a two weight local Tb theorem for any elliptic and gradient elliptic fractional singular integral operator T on the real line, and any pair of locally finite positive Borel measures on the line. This includes the Hilbert transform and in a sense improves on the T1 theorem by the authors and M. Lacey.
Cite
@article{arxiv.1709.09595,
title = {A two weight local Tb theorem for the Hilbert transform},
author = {Eric T. Sawyer and Chun-Yen Shen and Ignacio Uriarte-Tuero},
journal= {arXiv preprint arXiv:1709.09595},
year = {2019}
}
Comments
120 pages, 3 figures, 56 pages of appendices. We clarify arguments, mostly in appendix B, especially regarding the backward Poisson testing condition. We thank the referee for a thorough and insightful report. Main results unchanged