JournalsrmiVol. 29, No. 4pp. 1239–1262

On the boundedness of the Carleson operator near L1L^1

  • Victor Lie

    Purdue University, West Lafayette, USA
On the boundedness of the Carleson  operator near $L^1$ cover
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Abstract

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.

Cite this article

Victor Lie, On the boundedness of the Carleson operator near L1L^1. Rev. Mat. Iberoam. 29 (2013), no. 4, pp. 1239–1262

DOI 10.4171/RMI/755