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}
}
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5 pages