The Hilbert transform does not map L¹(Mw) to L^1,∞(w)

2010/11/08 by Reguera, Maria Carmen, Thiele, Christoph
#42B20 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1011.1767

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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