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

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

2002-11-22

arxiv.org/abs/math/0211363v1

Mathematics

Classical Analysis and ODEs

39 pages. Illinois Journal of Mathematics, to appear

Scientific paper

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 Sj\"olin's theorem on weak L^2 estimates for the maximal conjugated Calder\'on-Zygmund operator on R^n.

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