The T1 theorem for the Hilbert transform fails when p is not 2
Functional Analysis
2024-03-05 v2
Abstract
Given p between 1 and infinity, but not 2, we show that the T1 theorem for the Hilbert transform fails for L^{p}, despite holding for p equal to 2
Cite
@article{arxiv.2301.10046,
title = {The T1 theorem for the Hilbert transform fails when p is not 2},
author = {Michel Alexis and Jose Luis Luna-Garcia and Eric T. Sawyer and Ignacio Uriarte-Tuero},
journal= {arXiv preprint arXiv:2301.10046},
year = {2024}
}
Comments
4 pages. Misprints corrected, introduction modified to accurately reflect updated results in references. To appear in Journal d'Analyse Math\'ematique