L^p bounds for a maximal dyadic sum operator

2002/12/11 by Loukas Grafakos, Terence Tao, Grafakos, Loukas +3
Mathematics · #42A20 #42A24 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:42A20 #msc:42A24

paper · pdf · doi:10.48550/arxiv.math/0212164

16 pages, no figures, submitted, Math. Z

arxiv created 2002/12/11 · arxiv updated 2009/11/30

Abstract

We prove L^p bounds in the range 1<p<∞ for a maximal dyadic sum operator on \rn. This maximal operator provides a discrete multidimensional model of Carleson's operator. Its boundedness is obtained by a simple twist of the proof of Carleson's theorem given by Lacey and Thiele, adapted in higher dimensions by Pramanik and Terwilleger. In dimension one, the \lp boundedness of this maximal dyadic sum implies in particular an alternative proof of Hunt's extension of Carleson's theorem on almost everywhere convergence of Fourier integrals.

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