A Fefferman–Stein inequality for the Carleson operator

  1. Beltran Portales, David 1
  1. 1 Universitat de València
    info

    Universitat de València

    Valencia, España

    ROR https://ror.org/043nxc105

Journal:
Revista Matemática Iberoamericana

ISSN: 0213-2230,  2235-0616

Year of publication: 2018

Volume: 34

Issue: 1

Pages: 221-244

Type: Article

DOI: 10.4171/RMI/984 GOOGLE SCHOLAR lock_openOpen access editor

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Abstract

We provide a Fefferman–Stein type weighted inequality for maximally modulated Calderón–Zygmund operators that satisfy a priori weak type unweighted estimates. This inequality corresponds to a maximally modulated version of a result of Pérez. Applying it to the Hilbert transform we obtain the corresponding inequality for the Carleson operator C, that is C:Lp(M⌊p⌋+1w)→Lp(w) for any $1