Bulletin of the Belgian Mathematical Society - Simon Stevin

Hölder's inequality: some recent and unexpected applications

N. Albuquerque, G. Araújo, D. Pellegrino, and J.B. Seoane-Sepúlveda

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Abstract

Hölder'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 Hölder'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.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 24, Number 2 (2017), 199-225.

Dates
First available in Project Euclid: 23 August 2017

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1503453706

Digital Object Identifier
doi:10.36045/bbms/1503453706

Mathematical Reviews number (MathSciNet)
MR3693999

Zentralblatt MATH identifier
06850667

Subjects
Primary: 47A63: Operator inequalities 30B50: Dirichlet series and other series expansions, exponential series [See also 11M41, 42-XX] 46G25: (Spaces of) multilinear mappings, polynomials [See also 46E50, 46G20, 47H60] 46B70: Interpolation between normed linear spaces [See also 46M35] 47H60: Multilinear and polynomial operators [See also 46G25]

Keywords
Hölder's inequality random polynomials interpolation Bohr radius Kahane-Salem-Zygmund's inequality Quantum Information Theory, Hardy-Littlewood's inequality Bohnenblust-Hille's inequality Khinchine's inequality absolutely summing operators

Citation

Albuquerque, N.; Araújo, G.; Pellegrino, D.; Seoane-Sepúlveda, J.B. Hölder's inequality: some recent and unexpected applications. Bull. Belg. Math. Soc. Simon Stevin 24 (2017), no. 2, 199--225. doi:10.36045/bbms/1503453706. https://projecteuclid.org/euclid.bbms/1503453706


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