End-point estimates, extrapolation for multilinear Muckenhoupt classes, and applications

Kangwei Li, José María Martell, Henri Martikainen, Sheldy Ombrosi, Emil Vuorinen

Research output: Contribution to journalArticleScientificpeer-review


In this paper we present the results announced in the recent work by the first, second, and fourth authors of the current paper concerning Rubio de Francia extrapolation for the so-called multilinear Muckenhoupt classes. Here we consider the situations where some of the exponents of the Lebesgue spaces appearing in the hypotheses and/or in the conclusion can be possibly infinity. The scheme we follow is similar, but, in doing so, we need to develop a one-variable end-point off-diagonal extrapolation result. This complements the corresponding "finite" case obtained by Duoandikoetxea, which was one of the main tools in the aforementioned paper. The second goal of this paper is to present some applications. For example, we obtain the full range of mixed-norm estimates for tensor products of bilinear Calder'on-Zygmund operators with a proof based on extrapolation and on some estimates with weights in some mixed-norm classes. The same occurs with the multilinear Calder'on-Zygmund operators, the bilinear Hilbert transform, and the corresponding commutators with BMO functions. Extrapolation along with the already established weighted norm inequalities easily give scalar and vector-valued inequalities with multilinear weights and these include the end-point cases.

Original languageEnglish
JournalTransactions of the American Mathematical Society
Issue number1
Pages (from-to) 97-135
Number of pages39
Publication statusPublished - Jan 2021
MoE publication typeA1 Journal article-refereed

Fields of Science

  • 111 Mathematics
  • Multilinear Muckenhoupt weights
  • Rubio de Francia extrapolation
  • multilinear Calder'on-Zygmund operators
  • bilinear Hilbert transform
  • vector-valued inequalities
  • mixed-norm estimates

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