摘要
考虑空间C^(m,λ)(Ω__)的完备性和所嵌入的空间的问题,对Jensen不等式给出了直接的证明方法,利用Jensen不等式给出了Holder连续函数的例子。指出当Ω是非凸集时空间C1(Ω__)不能嵌入空间C^(0,λ)(Ω__)。给出C(Ω__)和C^(0,λ)(Ω__)是Banach空间证明的具体表述过程,通过建立Holder连续函数空间的插值空间的不等式,给出了空间C^(0,μ)(Ω__)嵌入的空间的证明;在Ω是Rn中的有界开集条件下,应用Arzela-Ascoli定理给出了空间C^(0,μ)(Ω__)紧嵌入的空间的证明,对相关经典知识给予了新的改造表述。
Considering the completeness of C^(m,λ)(Ω__) and the problem of embedded space,a direct proof method for Jensen inequality is given and the example of the continuous function of the Holder is given by using it. This paper pointed out that C^1(Ω__) can not embedded in space C^(0,λ)(Ω__) whenΩ is a non-convex set and the concrete proof is given that C(Ω__) and C^(0,λ)(Ω__) are Banach space; By establishing the inequality of interpolating space of the Holder continuous function space,the proof of the space C^(0,μ)(Ω__) can embedded in is given. Under the condition of Ω is bounded open set in Rn,the Arzela-Ascoli theorem is applied to give the proof of the space which C^(0,μ)(Ω__) tightly embed. A new and clear description of the relevant classical knowledge and forms a theoretical system is given in this paper.
出处
《四川理工学院学报（自然科学版）》
CAS
2018年第1期69-74,共6页
Journal of Sichuan University of Science & Engineering(Natural Science Edition)
基金
国家自然科学基金资助项目(11271040)
北京航空航天大学校级重大教改项目(201403)
关键词
Holder连续函数空间
插值不等式
嵌入定理
紧嵌入定理
Holder continuous function space
interpolation inequality
embedding theorem
compact embedding theorem
