Hölder不等式及其应用

Hölder’s Inequality and It’s Applications

摘要: 本文首先给出Young不等式的基本形式，在此基础上，证明经典的Hölder不等式的积分形式。在应用层面，选取函数估计、泛函极值、Minkowski不等式证明三个典型场景，展示Hölder不等式在分析问题中的具体用法，本文可作为学习Hölder不等式的补充材料。

Abstract: This paper begins with the basic form of Young’s inequality, based upon which the integral form of the classical Hölder inequality is established. Three typical applications are then presented—namely, function estimation, functional extremum problems, and the proof of Minkowski’s inequality—to illustrate the role of Hölder’s inequality in various analytical contexts. The paper is intended to serve as a supplementary reference for students and researchers studying Hölder’s inequality.