Quantitative estimates and extrapolation for multilinear weight classes

Bas Nieraeth*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

26 Citations (Scopus)
136 Downloads (Pure)


In this paper we prove a quantitative multilinear limited range extrapolation theorem which allows us to extrapolate from weighted estimates that include the cases where some of the exponents are infinite. This extends the recent extrapolation result of Li, Martell, and Ombrosi. We also obtain vector-valued estimates including ℓ spaces and, in particular, we are able to reprove all the vector-valued bounds for the bilinear Hilbert transform obtained through the helicoidal method of Benea and Muscalu. Moreover, our result is quantitative and, in particular, allows us to extend quantitative estimates obtained from sparse domination in the Banach space setting to the quasi-Banach space setting. Our proof does not rely on any off-diagonal extrapolation results and we develop a multilinear version of the Rubio de Francia algorithm adapted to the multisublinear Hardy–Littlewood maximal operator. As a corollary, we obtain multilinear extrapolation results for some upper and lower endpoints estimates in weak-type and BMO spaces.

Original languageEnglish
Pages (from-to)453-507
Number of pages55
JournalMathematische Annalen
Issue number1-2
Publication statusPublished - 8 Oct 2019


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