Hölder's inequality: some recent and unexpected applications

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 ho...

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Bibliographic Details
Authors: Alburquerque, N., Araujo, G., Pellegrino, Daniel, Seoane Sepúlveda, Juan Benigno
Format: article
Publication Date:2017
Country:España
Institution:Universidad Complutense de Madrid (UCM)
Repository:Docta Complutense
Language:English
OAI Identifier:oai:docta.ucm.es:20.500.14352/18092
Online Access:https://hdl.handle.net/20.500.14352/18092
Access Level:Open access
Keyword:517.98
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
Análisis funcional y teoría de operadores
Description
Summary: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.