Multilinear operators with non-smooth kernels and commutators of singular integrals

By Xuan Thinh Duong, Loukas Grafakos, Lixin Yan. 2009

79 citations recorded by the source corpus.

We obtain endpoint estimates for multilinear singular integral operators whose kernels satisfy regularity conditions significantly weaker than those of the standard Calder6n-Zygmund kernels. As a consequence, we deduce endpoint L 1 × ··· x L 1 to weak L 1/m estimates for the mth-order commutator of Calderon. Our results reproduce known estimates for m = 1, 2 but are new for m > 3. We also explore connections between the 2nd-order higher-dimensional commutator and the bilinear Hilbert transform and deduce some new off-diagonal estimates for the former.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/44ea187b06bd74678baa06dee6b47ba23d4c0687

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In Applied Mathematics

Citations in the corpus

Extrapolation for multilinear compact operators and applications (2020, methodology): “The results for the higher order were also presented in [31] and [32].”
Multilinear analysis on metric spaces (2014, methodology): “[60] Y. Han, D. Müller and D. Yang, A theory of Besov and Triebel-Lizorkin spaces on metric measure spaces modeled on Carnot-Carathéodory spaces, Abstr.”
Commutators of multilinear Calderón-Zygmund operators with kernels of Dini's type and applications (2019, unknown): “This topic was then further investigated by many authors in the last few decades, see for example [8, 12, 13, 14, 15, 16, 17, 19, 20, 22, 23].”