Multilinear singular integrals on non-commutative lp spaces
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 subc...
| Authors: | , , , |
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| Format: | article |
| Status: | Versión aceptada para publicación |
| Publication Date: | 2019 |
| Country: | España |
| Institution: | Basque Center for Applied Mathematics (BCAM) |
| Repository: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/1173 |
| Online Access: | http://hdl.handle.net/20.500.11824/1173 https://doi.org/10.1007/s00208-020-02068-4 |
| Access Level: | Open access |
| Keyword: | UMD spaces. representation theorems non- commutative spaces multilinear analysis singular integrals Calderón–Zygmund operators |
| Summary: | 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. |
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