Weak-L^p bounds for the Carleson and Walsh-Carleson operators

Francesco Di Plinio

doi:10.1016/j.crma.2014.02.005

Weak-L^p bounds for the Carleson and Walsh-Carleson operators

Classical Analysis and ODEs 2014-03-25 v2

Authors: Francesco Di Plinio

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Abstract

We prove a weak- $L^p$ bound for the Walsh-Carleson operator for $p$ near 1, improving on a theorem of Sjolin. We relate our result to the conjectures that the Walsh-Fourier and Fourier series of a function $f\in L\log L(\mathbb T)$ converge for almost every $x \in \mathbb T$ .

Keywords

Carleson operator Walsh-Carleson operator weak-$L^p$ bounds Walsh-Fourier series Fourier series convergence

Cite

@article{arxiv.1312.0398,
  title  = {Weak-L^p bounds for the Carleson and Walsh-Carleson operators},
  author = {Francesco Di Plinio},
  journal= {arXiv preprint arXiv:1312.0398},
  year   = {2014}
}

Comments

11 pages, with a 5 pages appendix. An abridged version (without appendix) of this article has been accepted for publication on Comptes Rendus Mathematiques

Weak-L^p bounds for the Carleson and Walsh-Carleson operators

Abstract

Keywords

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