Revista Matemática Iberoamericana


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Volume 34, Issue 1, 2018, pp. 221–244
DOI: 10.4171/RMI/984

Published online: 2018-02-06

A Fefferman–Stein inequality for the Carleson operator

David Beltran[1]

(1) University of Birmingham, UK

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 $\mathcal{C}$, that is $\mathcal{C}\colon L^p(M^{\lfloor p \rfloor +1}w) \to L^p(w)$ for any $1

Keywords: Carleson operator, weighted inequality, sparse operators, maximal operators

Beltran David: A Fefferman–Stein inequality for the Carleson operator. Rev. Mat. Iberoam. 34 (2018), 221-244. doi: 10.4171/RMI/984