Hölder不等式：一些最近和意想不到的应用
Hölder's inequality: some recent and unexpected applications
摘要：
霍德不等式，因为它的外观在1888年，发挥了根本性的作用，在数学分析，它是毫无疑问，一个里程碑式的数学。这似乎很奇怪，如今，它不断重新出现，并为数学界带来新的见解。在这篇简短的文章中，我们将展示如何在泛函分析中基本上忽略了Hölder不等式的一个变体（尽管在偏微分方程中很有名），并且在数学最近的重大突破中产生了至关重要的（在某种意义上是意想不到的）影响。其中一些最新进展出现在2012-2014年，包括狄利克雷级数理论，著名的玻尔半径问题，某些经典不等式（如Bohnenblust-Hille或Hardy-Littlewood），甚至数学物理。
英文摘要：
Hölder's inequality, since its appearance in 1888, has played a fundamental role in Mathematical Analysis and it is, without any doubt, one of the milestones in Mathematics. It may seem strange that, nowadays, it keeps resurfacing and bringing new insights to the mathematical community. In this expository article we show how a variant of Hölder's inequality (although well-known in PDEs) was essentially overlooked in Functional Analysis and has had a crucial (and in some sense unexpected) influence in very recent and major breakthroughs in Mathematics. Some of these recent advances appeared in 2012-2014 and include the theory of Dirichlet series, the famous Bohr radius problem, certain classical inequalities (such as Bohnenblust--Hille or Hardy--Littlewood), or even Mathematical Physics.
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