L^1空间中紧算子的一个注记  

A Notation of a Compact Operator in L^1 Space

作　　者：岳铭 王佳[2] 王辉[1] 张欣[3] 任寒景 YUE Ming;WANG Jia;WANG Hui;ZHANG Xin;REN Hanjing(College of Mathematical Sciences,Harbin Normal University,Harbin 150025,China;College of Science,Northeast Agricultural University,Harbin 150030,China;Department of Basic Courses,Beijing Union University,Beijing 100101,China;School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China;Key Laboratory of Systems and Control,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China)

机构地区：[1]哈尔滨师范大学数学科学学院,哈尔滨150025 [2]东北农业大学理学院,哈尔滨150030 [3]北京联合大学基础课教学部,北京100101 [4]中国科学院大学数学科学学院,北京100049 [5]中国科学院数学与系统科学研究院系统控制实验室,北京100190

出　　处：《应用泛函分析学报》2020年第1期44-50,共7页Acta Analysis Functionalis Applicata

基　　金：黑龙江省自然科学基金(A201305);北京市教委科研计划项目(KM201811417013)。

摘　　要：由于具有有界可测核函数的积分算子不能保证在L[0,1]^1上是紧算子,本文证明了当d(s)和b(t)是有界可测函数,G(s,t)是连续函数时,一类弱奇异核函数K1(s,t)=d(s)G(s,t)b(t)/|s-t|^α(0<α<1)对应的积分算子K1:(K(1φ))(s)=∫0^1 K1(s,t)φ(t)dt在L([0,1])^1上产生一个紧算子,并给出了一个具体的弱奇异函数对应积分算子的紧性证明.An integral operator with a bounded measurable kernel function is not necessarily a compact operator in L[0,1]^1 space.This paper proves that the integral operator K1(s,t)=d(s)G(s,t)b(t)/|s-t|^α(0<α<1) of one class of weakly singular kernel function K1:(K(1φ))(s)=∫0^1 K1(s,t)φ(t) is a compact operator in L1[0;1]when the d(s)and b(t)are bounded measurable functions,and G(s,t)is a continuous function.And then,the latter part proves that a integral operator of a speci c weakly singular kernel function is compact.

关 键 词：紧算子 弱奇异核函数 有界可测 L^1空间 一维 

分 类 号：O177.6[理学—数学]