某类Nehari函数族的边界性质  

Boundary Properties of Nehari Function Families

作　　者：谢志春 李东征 XIE Zhichun;LI Dongzheng(Department of Mathematics,Xiamen Institute of Technology,Xiamen 361021,China;Common Course Department,Xiamen Medical College,Xiamen 361023,China)

机构地区：[1]厦门工学院数学系,福建厦门361021 [2]厦门医学院公共课教学部,福建厦门361023

出　　处：《厦门理工学院学报》2020年第1期85-88,共4页Journal of Xiamen University of Technology

基　　金：福建省中青年教师教育科研项目(JAT170807,JAT170812);厦门工学院科研项目(KY2017004,KY2017009)。

摘　　要：为更全面地了解不同参数Nehari函数族的边界性质,利用Nehari函数及其导数的偏差性质,采用分析构造法研究参数α∈1,2]的函数族的边界性质。研究发现:对于该类函数族中满足规范条件的任一函数的一阶和二阶导数,除了可列个点外,均满足lim infr→1(1-r^2)Re{ζf″/f′(rζ)}<2α,ζ=1;同时,对于ζ=1,r∈(0,1),有|f(ζ)-f(rζ)|≤(1-r^2)|f′(rζ)|αr-1-r^22Reζf″/f′(rζ)。当α=1时,以上两个结论与Chuaqui的结论一致。To have a better understanding of the boundary properties of Nehari function family with different parameters,boundary property of Nehari function family withα∈[1,2]is investigated with the deviation property of the functions and their derivatives in this paper.The result for lim infr→1(1-r^2)Reζf″[]f′(rζ)<2α,ζ=1 with f∈N0 is established except for the points that can be listed and|f(ζ)-f(rζ)|≤(1-r^2)|f′(rζ)|αr-1-r^22Reζf″[]f′(rζ)withζ=1,r∈(0,1)is obtained.The two conclusions are consistent with the corresponding ones by Chuaqui withα=1.

关 键 词：Nehari函数族 边界性质 SCHWARZ导数 偏差性质 分析构造法 

分 类 号：O174.55[理学—数学]