Revista Matemática Iberoamericana

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Volume 29, Issue 4, 2013, pp. 1239–1262
DOI: 10.4171/RMI/755

Published online: 2013-12-15

On the boundedness of the Carleson operator near $L^1$

Victor Lie[1]

(1) Purdue University, West Lafayette, USA

Based on the tile discretization elaborated in [14], 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.

Keywords: Time-frequency analysis, Carleson’s theorem

Lie Victor: On the boundedness of the Carleson operator near $L^1$. Rev. Mat. Iberoam. 29 (2013), 1239-1262. doi: 10.4171/RMI/755