Multilinear singular integrals on non-commutative Lp spaces

Research output: Contribution to journalArticle

Abstract

We prove Lp bounds for the extensions of standard multilinear Calderón–Zygmund operators to tuples of UMD spaces tied by a natural product structure. The product can, for instance, mean the pointwise product in UMD function lattices, or the composition of operators in the Schatten-von Neumann subclass of the algebra of bounded operators on a Hilbert space. We do not require additional assumptions beyond UMD on each space—in contrast to previous results, we e.g. show that the Rademacher maximal function property is not necessary. The obtained generality allows for novel applications. For instance, we prove new versions of fractional Leibniz rules via our results concerning the boundedness of multilinear singular integrals in non-commutative Lp spaces. Our proof techniques combine a novel scheme of induction on the multilinearity index with dyadic-probabilistic techniques in the UMD space setting.

Details

Authors
  • Francesco Di Plinio
  • Kangwei Li
  • Henri Martikainen
  • Emil Vuorinen
Organisations
External organisations
  • Washington University in St. Louis
  • Tianjin University
  • Basque Center of Applied Mathematics
  • University of Helsinki
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics

Keywords

  • Calderón–Zygmund operators, Multilinear analysis, Non-commutative spaces, Representation theorems, Singular integrals, UMD spaces
Original languageEnglish
JournalMathematische Annalen
Publication statusPublished - 2020 Sep 4
Publication categoryResearch
Peer-reviewedYes