Multilinear singular integrals on non-commutative Lp spaces

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Multilinear singular integrals on non-commutative Lp spaces. / Di Plinio, Francesco; Li, Kangwei; Martikainen, Henri; Vuorinen, Emil.

In: Mathematische Annalen, 04.09.2020.

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Di Plinio, Francesco ; Li, Kangwei ; Martikainen, Henri ; Vuorinen, Emil. / Multilinear singular integrals on non-commutative Lp spaces. In: Mathematische Annalen. 2020.

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TY - JOUR

T1 - Multilinear singular integrals on non-commutative Lp spaces

AU - Di Plinio, Francesco

AU - Li, Kangwei

AU - Martikainen, Henri

AU - Vuorinen, Emil

PY - 2020/9/4

Y1 - 2020/9/4

N2 - 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.

AB - 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.

KW - Calderón–Zygmund operators

KW - Multilinear analysis

KW - Non-commutative spaces

KW - Representation theorems

KW - Singular integrals

KW - UMD spaces

UR - http://www.scopus.com/inward/record.url?scp=85090243283&partnerID=8YFLogxK

U2 - 10.1007/s00208-020-02068-4

DO - 10.1007/s00208-020-02068-4

M3 - Article

AN - SCOPUS:85090243283

JO - Mathematische Annalen

JF - Mathematische Annalen

SN - 0025-5831

ER -