Sharp Weighted Bounds for Multilinear Maximal Functions and Calderón–Zygmund Operators
By W. Damián, Andrei K. Lerner, C. P'erez. 2012
66 citations recorded by the source corpus.
In this paper we prove some sharp weighted norm inequalities for the multi(sub)linear maximal function $$\mathcal {M}$$M introduced in Lerner et al. (Adv Math 220:1222–1264, 2009) and for multilinear Calderón–Zygmund operators. In particular we obtain a sharp mixed “$$A_p-A_{\infty }$$Ap-A∞” bound for $$\mathcal {M}$$M, some partial results related to a Buckley-type estimate for $$\mathcal {M}$$M, and a sufficient condition for the boundedness of $$\mathcal {M}$$M between weighted $$L^p$$Lp spaces with different weights taking into account the precise bounds. Next we get a bound for multilinear Calderón–Zygmund operators in terms of dyadic positive multilinear operators in the spirit of the recent work (Lerner, J Anal Math 121:141–161, 2013). Then we obtain a multilinear version of the “$$A_2$$A2 conjecture”. Several open problems are posed.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/1d59c429f6fcc31b3f80eab76039ab429985d86b
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In Applied Mathematics
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Citations in the corpus
- Extrapolation for multilinear Muckenhoupt classes and applications (2018, background): “To proceed we follow an argument in [15], see also [29], which in turn is a bilinear extension of the linear case proof in [13].”
- The Sharp Weighted Bound for Multilinear Maximal Functions and Calderón–Zygmund Operators (2012, methodology): “Q ∈ S there exists EQ ⊂ Q such that {EQ}Q∈S is pairwise disjoint and |EQ| ≥ 1 2|Q|. Sparse families have long played a role in Calder´on-Zygmund theory, our definition can be found in [9]. Finally, in [5], the multilinear sparse operators, AD,S(f~) = X Q∈S Ym i=1 1 |Q| Z Q fi χQ, were defined and use”