2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65759Lacey 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 appearClassical Analysis and ODEs42B20;42B25text