Multilinear singular integrals on non-commutative Lp spaces
(2020) In Mathematische Annalen- 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... (More)
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.
(Less)
- author
- Di Plinio, Francesco ; Li, Kangwei ; Martikainen, Henri and Vuorinen, Emil LU
- organization
- publishing date
- 2020-09-04
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Calderón–Zygmund operators, Multilinear analysis, Non-commutative spaces, Representation theorems, Singular integrals, UMD spaces
- in
- Mathematische Annalen
- publisher
- Springer
- external identifiers
-
- scopus:85090243283
- ISSN
- 0025-5831
- DOI
- 10.1007/s00208-020-02068-4
- language
- English
- LU publication?
- yes
- id
- 7ceb6896-7b83-4280-afa1-ddc01e6eb712
- date added to LUP
- 2020-09-24 18:46:44
- date last changed
- 2022-04-19 00:55:12
@article{7ceb6896-7b83-4280-afa1-ddc01e6eb712,
abstract = {{<p>We prove L<sup>p</sup> 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 L<sup>p</sup> spaces. Our proof techniques combine a novel scheme of induction on the multilinearity index with dyadic-probabilistic techniques in the UMD space setting.</p>}},
author = {{Di Plinio, Francesco and Li, Kangwei and Martikainen, Henri and Vuorinen, Emil}},
issn = {{0025-5831}},
keywords = {{Calderón–Zygmund operators; Multilinear analysis; Non-commutative spaces; Representation theorems; Singular integrals; UMD spaces}},
language = {{eng}},
month = {{09}},
publisher = {{Springer}},
series = {{Mathematische Annalen}},
title = {{Multilinear singular integrals on non-commutative L<sup>p</sup> spaces}},
url = {{http://dx.doi.org/10.1007/s00208-020-02068-4}},
doi = {{10.1007/s00208-020-02068-4}},
year = {{2020}},
}