CAJ | 학술논문

著名的Holder不等式在数学分析、调和分析、泛函分析以及偏微分方程等学科的研究中发挥着重要作用．该不等式不仅使用技巧灵活，而且得到的结果极其深刻．本文首先在可测函数论的基础上，给出Holder不等式的一种新的证明方法，然后利用数学归纳法导出Holder不等式的推广形式，最后应用Holder不等式得出两个重要结论，为该不等式在更广数学领域的研究和应用奠定了基础．
저명적Holder불등식재수학분석、조화분석、범함분석이급편미분방정등학과적연구중발휘착중요작용．해불등식불부사용기교령활，이차득도적결과겁기심각．본문수선재가측함수론적기출상，급출Holder불등식적일충신적증명방법，연후이용수학귀납법도출Holder불등식적추엄형식，최후응용Holder불등식득출량개중요결론，위해불등식재경엄수학영역적연구화응용전정료기출．
Famous Holder inequality plays an important role in the study of some disciplines such as mathematical analysis, harmonic analysis, functional analysis and partial differential equations. Not only its tips for using are flexibly, but also the results are very impressive. In this paper,a new method to prove Holder inequality on the basis of measurable functions was given. And generalized Holder inequality is given using mathematical induction forms. Last two important conclusions based on Holder inequality were got. These eonelusions lays the foundation for the equality＇s researches and applica- tions in the wider mathematics areas.