L^(2)空间中一个不等式的最优常数和取等条件问题  

A Problem on Optimal Constant and Equal Condition of an Inequality in L^(2) Space

作　　者：赖宝锋 陈明玉[1] LAI Baofeng;CHEN Mingyu(School of Mathematics and Computer Science,Quanzhou Normal University,Quanzhou 362000,China)

机构地区：[1]泉州师范学院数学与计算机科学学院,福建泉州362000

出　　处：《泉州师范学院学报》2022年第5期38-44,共7页Journal of Quanzhou Normal University

基　　金：福建省教育科技类项目(JAT210305)

摘　　要：文章分析了L^(2)空间中一类不等式的最优常数和取等条件.首先,对L^(2)空间进行正交分解,将所考虑的问题转化为与实二次型有关的泛函最值问题.其次,利用实二次型理论解决此最值问题.所得结果完全解决了《美国数学月刊》2022年4月征解的问题12318.In the paper,we consider the optimal constant and equal condition of a class of inequalities in L^(2)space.First,the L^(2)space was orthogonal decomposed,and the problem was transformed into a functional maximum problem related to real quadratic form.Secondly,the real quadratic form theory is used to solve this maximum problem.The obtained results showed that the problem 12318 which proposed in April 2022 by American Mathematical Monthly was completely solved.

关 键 词：正交分解 L^(2)空间 实二次型 最优常数 取等条件 

分 类 号：O177[理学—数学]