L^p bounds for a maximal dyadic sum operator

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We prove $L^p$ bounds in the range $1<p<\infty$ 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.
16 pages, no figures, submitted, Math. Z

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Classical Analysis and ODEs, 42A20; 42A24

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http://salesiana.dossiersoluciones.com/handle/123456789/65963

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0212164
 http://arxiv.org/abs/math/0212164

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arXiv