Banach-valued multilinear singular integrals with modulation invariance

Francesco Di Plinio, Kangwei Li, Henri Martikainen, Emil Vuorinen

Research output: Contribution to journalArticleScientificpeer-review


We prove that the class of trilinear multiplier forms with singularity over a one-dimensional subspace, including the bilinear Hilbert transform, admits bounded L-p-extension to triples of intermediate UMD spaces. No other assumption, for instance of Rademacher maximal function type, is made on the triple of UMD spaces. Among the novelties in our analysis is an extension of the phase-space projection technique to the UMD-valued setting. This is then employed to obtain appropriate single-tree estimates by appealing to the UMD-valued bound for bilinear Calderon-Zygmund operators recently obtained by the same authors.

Original languageEnglish
JournalInternational Mathematics Research Notices
Issue number7
Pages (from-to)5256–5319
Number of pages64
Publication statusPublished - 23 Mar 2022
MoE publication typeA1 Journal article-refereed

Fields of Science

  • UMD
  • 111 Mathematics

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