$A_p$-$A_{\infty }$ estimates for multilinear maximal and sparse operators

Abstract

We obtain mixed $A_p$--$A_{\infty }$ estimates for a large family of multilinear maximal and sparse operators. Operators from this family are known to control for instance multilinear Calderón--Zygmund operators, square functions, fractional integrals, and the bilinear Hilbert transform. Our results feature a new multilinear version of the Fujii--Wilson $A_{\infty }$ characteristic that allows us to recover the best known estimates in terms of the $A_p$ characteristic for dependent weights as a special case of the mixed characteristic estimates for general tuples of weights.

v2: main results restricted to sparse collections because the proof of Lemma 2.4 does not work for general Carleson sequences

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Cited by in corpus (3)

• Dyadic harmonic analysis and weighted inequalities: the sparse revolution
• Sparse bounds for maximal rough singular integrals via the Fourier transform
• Weak and strong type estimates for the multilinear Littlewood-Paley operators