On the Boundedness of the Carleson Operator near $L^1$

Details On the Boundedness of the Carleson Operator near $L^1$ On the Boundedness of the Carleson Operator near $L^1$

2011-12-20

arxiv.org/abs/1112.4573v1

Mathematics

Classical Analysis and ODEs

21 pages, no figures. Submitted

Scientific paper

Based on the tile discretization elaborated by the author in "The Polynomial Carleson Operator", we develop a Calderon-Zygmund type decomposition of the Carleson operator. As a consequence, through a unitary method that makes no use of extrapolation techniques, we recover the previously known results regarding the largest rearrangement invariant space of functions with almost everywhere convergent Fourier series.

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