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一类非齐次核的Hilbert型级数算子最佳搭配参数的充要条件
引用本文:洪勇,陈强. 一类非齐次核的Hilbert型级数算子最佳搭配参数的充要条件[J]. 数学的实践与认识, 2022, 0(1): 216-222
作者姓名:洪勇  陈强
作者单位:1.广州华商学院应用数学系;2.广东第二师范学院计算机科学系
基金项目:国家自然科学基金(61772140)。
摘    要:选择搭配参数a,b,利用权函数方法,可得核为K(m,n)的级数算子T的不等式:||T((a))||p,β(a,b) ≤ M(a,b)||(a)||p,α(a,b),(a) ={am}一般地,M(a,b)并不是T:lap(a,b)→lβp(a,b)的算子范数,针对非齐次核K(m,n)=G(mλ1/nλ2)(λ1λ2>0)...

关 键 词:Hilbert型级数算子  Hilbert型级数不等式  非齐次核  算子范数  最佳搭配参数

The Necessary and Sufficient Conditions for Optimal Matching Parameters of Hilbert-Type Series Operator with a Class of Non-Homogeneous Kernel
HONG Yong,CHEN Qiang. The Necessary and Sufficient Conditions for Optimal Matching Parameters of Hilbert-Type Series Operator with a Class of Non-Homogeneous Kernel[J]. Mathematics in Practice and Theory, 2022, 0(1): 216-222
Authors:HONG Yong  CHEN Qiang
Affiliation:(Department of Applied Mathematics,Guangzhou Huashang College,Guangzhou 511300,China;Department of Computer Science,Guangdong University of Education,Guangzhou 510303,China)
Abstract:By choosing the matching parameters a and b,using the weight function method,the inequality of series operator T with kernel K(m,n):‖T(a)‖p,β(a,B)≤M(a,b)‖a‖p,α(a,b)can be obtained.In general M(a,b)is not the norm of operator T:lpα(a,b)→lpβ(a,b).using the weight function method the paper discusses the necessary and sufficient conditions of the best matching parameters for operator T with non-homogeneous kernel K(m,n)=G(mλ1/nλ2)(λ1λ2>0),and obtaied the norm formula of operator T when a and b are the best matching parameters.
Keywords:Hilbert-type series operator  Hilbert-type series inequality  non-homogeneous kernel  operator norm  the best matching parameter
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