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Banach-Valued Multilinear Singular Integrals with Modulation Invariance

Di Plinio, Francesco ; Li, Kangwei ; Martikainen, Henri and Vuorinen, Emil LU (2022) In International Mathematics Research Notices 2022(7). p.5256-5319
Abstract

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 operatorname 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 Calderón-Zygmund operators recently obtained by the same authors.

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author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
International Mathematics Research Notices
volume
2022
issue
7
pages
5256 - 5319
publisher
Oxford University Press
external identifiers
  • scopus:85127980265
ISSN
1073-7928
DOI
10.1093/imrn/rnaa234
language
English
LU publication?
yes
id
e7c1849f-d466-4307-9cd0-fd38a9c39e6e
date added to LUP
2022-06-09 11:20:31
date last changed
2022-06-09 11:20:31
@article{e7c1849f-d466-4307-9cd0-fd38a9c39e6e,
  abstract     = {{<p>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 operatorname 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 Calderón-Zygmund operators recently obtained by the same authors. </p>}},
  author       = {{Di Plinio, Francesco and Li, Kangwei and Martikainen, Henri and Vuorinen, Emil}},
  issn         = {{1073-7928}},
  language     = {{eng}},
  month        = {{04}},
  number       = {{7}},
  pages        = {{5256--5319}},
  publisher    = {{Oxford University Press}},
  series       = {{International Mathematics Research Notices}},
  title        = {{Banach-Valued Multilinear Singular Integrals with Modulation Invariance}},
  url          = {{http://dx.doi.org/10.1093/imrn/rnaa234}},
  doi          = {{10.1093/imrn/rnaa234}},
  volume       = {{2022}},
  year         = {{2022}},
}