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arXiv · 1112.4573

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

Victor Lie
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Abstract

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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Victor Lie. 2012-08-10. On the Boundedness of the Carleson Operator near $L^1$. https://arxiv.org/abs/1112.4573

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