一类加权序列空间中广义齐次核的Hilbert型离散不等式和序列算子的有界性  

The hilbert-type discrete inequalities with generalized homogeneous kernel and boundedness of sequence operators in a class of weighted sequence spaces

作　　者：张丽娟 洪勇 孔荫莹 ZHANG Lijuan;HONG Yong;KONG Yinying(College of Data Science,Guangzhou Huashang college,Guangzhou 511300,China;College of Statistics and Mathematics,Guangdong University of Finance and Economics,Guangzhou 510320,China)

机构地区：[1]广州华商学院数据科学学院,广东广州511300 [2]广东财经大学统计与数学学院,广东广州510320

出　　处：《南昌大学学报（理科版）》2023年第4期312-316,327,共6页Journal of Nanchang University(Natural Science)

基　　金：广东省基础与应用基础研究基金(2022A1515012429);广州华商学院导师制项目(2023HSDS04).

摘　　要：引入以指数函数为权函数的加权序列空间l_(r)^(φ(m))(Z),通过权系数方法,得到加权序列空间中具有广义齐次核的Hilbert型离散不等式,利用所得不等式讨论加权序列空间中序列算子的有界性及算子范数估计,并给出若干特例.The weighted sequence space with the exponential function as the weight function was introduced,the Hilbert-type discrete inequality with generalized homogeneous Kernel in the weighted sequence space was obtained by the power coefficient method,and the resulting inequality was used to discuss the boundedness and norm estimate of sequence operators in the weighted sequence space,and several special cases were given.

关 键 词：加权序列空间 Hilbert型离散不等式 广义齐次核 序列算子 有界算子 算子范数 

分 类 号：O178[理学—数学]