Besov空间中Gauss-Weierstrass算子的正逆定理  

Direct and Inverse Theorems of Gauss-Weierstrass Operators in Besov Space

作　　者：官心果 钟宇 何翠玲 吴晓刚[2] GUAN Xin-guo;ZHONG Yu;HE Cui-ling;WU Xiao-gang(School of Mathematics and Computer Science,Yunnan Minzu University,Kunming 650500,China;School of Information Technology,Xingyi Normal University for Nationalities,Xingyi Guizhou 562400,China)

机构地区：[1]云南民族大学数学与计算机科学学院,昆明650500 [2]兴义民族师范学院信息与技术学院,贵州兴义562400

出　　处：《西南大学学报（自然科学版）》2020年第10期109-115,共7页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金项目(11361076);贵州省教育厅重点项目(黔教合KY[2015]403).

摘　　要：在研究关于Gauss-Weierstrass算子的Lp-逼近的基础之上,结合算子范数插值定理,继续研究推导了Gauss-Weierstrass算子在Bp,q^s,Lp上的性质、定理.借助K-泛函,给出Gauss-Weiersttrass算子在Besov空间中的逼近,得出Besov空间中Gauss-Weierstrass算子的正逆定理,并对Besov空间进行刻画.On the basis of research on the Lp approximation of Gauss-Weierstrass operator,combined with the interpolation theorem of operator norm,the properties and theorems of Gauss-Weierstrass operators in Bp,q^s and Lp are further studied and deduced.By means of K-functional,the approximation of the Gauss-Weiersttrass operator in Besov space is given,and the positive and negative theorems of the Gauss-Weierstrass operator in Besov space are obtained,and the Besov space is described.

关 键 词：K-泛函 Gauss-Weiersttrass算子 BESOV空间 

分 类 号：O174.41[理学—数学]