Hölder's inequality: some recent and unexpected applications



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Alburquerque, N. and Araujo, G. and Pellegrino, D. and Seoane-Sepúlveda, Juan B. (2017) Hölder's inequality: some recent and unexpected applications. Bulletin of the Belgian Mathematical Society - Simon Stevin, 24 (2). pp. 199-225. ISSN 1370-1444

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Official URL: https://projecteuclid.org/euclid.bbms/1503453706


Holder's inequality, since its appearance in 1888, has played a fundamental role in Mathematical Analysis and may be considered a milestone in Mathematics. It may seem strange that, nowadays, it keeps resurfacing and bringing new insights to the mathematical community. In this survey we show how a variant of Holder's inequality (although well-known in PDEs) was essentially overlooked in Functional/Complex Analysis and has had a crucial (and in some sense unexpected) influence in very recent advances in different fields of Mathematics. Some of these recent advances have been appearing since 2012 and include the theory of Dirichlet series, the famous Bohr radius problem, certain classical inequalities (such as Bohnenblust-Hille or Hardy-Littlewood), and Mathematical Physics.

Item Type:Article
Uncontrolled Keywords:Hölder’s inequality; Minkowki’s inequality; Interpolation; Bohr radius; Quantum Information Theory; Hardy-Littlewood’s inequality; Bohnenblust-Hille’s inequality; Khinchine’s inequality; Kahane-Salem-Zygmund’s inequality; Absolutely summing operators
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:44730
Deposited On:22 Sep 2017 11:19
Last Modified:25 Sep 2017 08:26

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