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april 2017 Hölder's inequality: some recent and unexpected applications
N. Albuquerque, G. Araújo, D. Pellegrino, J.B. Seoane-Sepúlveda
Bull. Belg. Math. Soc. Simon Stevin 24(2): 199-225 (april 2017). DOI: 10.36045/bbms/1503453706

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.

Citation

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N. Albuquerque. G. Araújo. D. Pellegrino. J.B. Seoane-Sepúlveda. "Hölder's inequality: some recent and unexpected applications." Bull. Belg. Math. Soc. Simon Stevin 24 (2) 199 - 225, april 2017. https://doi.org/10.36045/bbms/1503453706

Information

Published: april 2017
First available in Project Euclid: 23 August 2017

zbMATH: 06850667
MathSciNet: MR3693999
Digital Object Identifier: 10.36045/bbms/1503453706

Subjects:
Primary: 30B50, 46B70, 46G25, 47A63, 47H60‎

Rights: Copyright © 2017 The Belgian Mathematical Society

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Vol.24 • No. 2 • april 2017
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