On the Boundedness of the Carleson Operator near L¹

2011/12/20 by Victor Lie, Lie, Victor
Mathematics · #42A20 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.1112.4573

openalex publication_date 2011/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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