A WEAK L~2 ESTIMATE FOR A MAXIMAL DYADIC SUM OPERATOR ON R~n

摘要

Lacey and Thiele recently obtained a new proof of Car-leson'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 Sjoelin's theorem on weak L~2 estimates for the maximal conjugated Calderon-Zygmund operator on R~n.