English

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

R2 v1 2026-06-28T08:18:42.407Z