摘要
本文讨论了三维弱奇异核积分算子K:■其中■0<α<3,■是Ω×Ω上的连续函数.证明了当0<α<3时,K是从L^1(Ω)空间到L^1(Ω)空间中的紧算子.
In this paper, we consider the compactness of three-dimensional weakly singular integral operators K:(Kφ)(s→)=∫ΩK(s→,t→)φ(t→)dt→,s→∈[0,1]^3=Ωwhere K(s→,t→)=G(s→,t→)/|s→,t→|α,0<α<3, and G(s,t) is continuous on(s,t)∈Ω×Ω. We prove that K is a compact operator from L^1(Ω) space to L^1(Ω) space.
作者
张欣
任寒景
朱广田
ZHANG Xin;REN Hanjing;ZHU Guangtian(Department of Basic Courses,Beijing Union University,Beijing 100101,China;Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China)
出处
《应用泛函分析学报》
2019年第1期1-7,共7页
Acta Analysis Functionalis Applicata
基金
北京市教委科研计划项目(KM201811417013)
关键词
三维
弱奇异积分算子
紧性
three-dimensional
weakly singular integral operators
compactness
