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Disentanglement,
multilinear duality and factorisation for nonpositive
operators
Anthony Carbery, Timo S. Hänninen and Stefán Ingi Valdimarsson |
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Vol. 16 (2023), No. 2, 511–543
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Abstract |
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In a previous work we established a multilinear duality and factorisation theory for norm inequalities for pointwise weighted geometric means of positive linear operators defined on normed lattices. In this paper we extend the reach of the theory for the first time to the setting of general linear operators defined on normed spaces. The scope of this theory includes multilinear Fourier restriction-type inequalities. We also sharpen our previous theory of positive operators. Our results all share a common theme: estimates on a weighted geometric mean of linear operators can be disentangled into quantitatively linked estimates on each operator separately. The concept of disentanglement recurs throughout the paper. The methods we used in the previous work — principally convex optimisation — relied strongly on positivity. In contrast, in this paper we use a vector-valued reformulation of disentanglement, geometric properties (Rademacher-type) of the underlying normed spaces, and probabilistic considerations related to -stable random variables. |
Keywords
multilinear inequalities, duality, factorisation,
disentanglement, $p$-convexity, Rademacher-type
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Mathematical Subject Classification
Primary: 42B99, 46B99, 47H99
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Milestones
Received: 18 September 2020
Revised: 9 July 2021
Accepted: 11 August 2021
Published: 3 May 2023
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Authors |
| Anthony Carbery | |
| School of Mathematics and Maxwell
Institute for Mathematical Sciences University of Edinburgh Edinburgh United Kingdom |
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| Timo S. Hänninen | |
| Department of Mathematics and
Statistics University of Helsinki Helsinki Finland |
School of Mathematics and Maxwell
Institute for Mathematical Sciences University of Edinburgh Edinburgh United Kingdom |
| Stefán Ingi Valdimarsson | |
| Arion banki Reykjavík Iceland |
Science Institute, Mathematics
Division University of Iceland Reykjavík Iceland |
| © 2023 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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