English

The Hilbert transform does not map L^1(Mw) to L^{1,\infty}(w)

Classical Analysis and ODEs 2010-11-09 v1

Abstract

We prove that the analogue for the Hilbert transform of a classical weighted inequality by Fefferman and Stein for the Hardy Littlewood maximal operator does not hold. This is a sequel to paper arXiv:1008.3943 by the first author, which shows the same for the general Haar multiplier operator.

Keywords

Cite

@article{arxiv.1011.1767,
  title  = {The Hilbert transform does not map L^1(Mw) to L^{1,\infty}(w)},
  author = {Maria Carmen Reguera and Christoph Thiele},
  journal= {arXiv preprint arXiv:1011.1767},
  year   = {2010}
}

Comments

5 pages

R2 v1 2026-06-21T16:40:27.611Z