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...
| Authors: | , , , |
|---|---|
| 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 |
| 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. |
|---|