Based on the tile discretization elaborated in , we develop a Calderón–Zygmund type decomposition of the Carleson operator. As a consequence, through a unitary method that makes no use of extrapolation techniques, we recover previously known results regarding the largest rearrangement invariant space of functions with almost everywhere convergent Fourier series.
Cite this article
Victor Lie, On the boundedness of the Carleson operator near . Rev. Mat. Iberoam. 29 (2013), no. 4, pp. 1239–1262DOI 10.4171/RMI/755