A weak L^2 estimate for a maximal dyadic sum operator on R^n

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Lacey and Thiele have recently obtained a new proof of Carleson's theorem on almost everywhere convergence of Fourier series. This paper is a generalization of their techniques (known broadly as time-frequency analysis) to higher dimensions. In particular, a weak-type (2,2) estimate is derived for a maximal dyadic sum operator on R^n, n > 1. As an application one obtains a new proof of Sjölin's theorem on weak L^2 estimates for the maximal conjugated Calderón-Zygmund operator on R^n.
39 pages. Illinois Journal of Mathematics, to appear

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Classical Analysis and ODEs, 42B20;42B25

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http://salesiana.dossiersoluciones.com/handle/123456789/65759

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0211363
 http://arxiv.org/abs/math/0211363

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arXiv