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arXiv · 1011.1767

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

Maria Carmen Reguera·Christoph Thiele
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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.

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Maria Carmen Reguera, Christoph Thiele. 2010-11-08. The Hilbert transform does not map L^1(Mw) to L^{1,\infty}(w). https://arxiv.org/abs/1011.1767

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