A Fefferman–Stein inequality for the Carleson operator
David Beltran
University of Birmingham, UK
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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 , that is for any and any weight function , with bound independent of . We also provide a maximal-multiplier weighted theorem, a vector-valued extension, and more general two-weighted inequalities. Our proof builds on a recent work of Di Plinio and Lerner combined with some results on Orlicz spaces developed by Pérez.
Cite this article
David Beltran, A Fefferman–Stein inequality for the Carleson operator. Rev. Mat. Iberoam. 34 (2018), no. 1, pp. 221–244
DOI 10.4171/RMI/984