一类非齐次核的Hilbert型级数算子最佳搭配参数的充要条件

The Necessary and Sufficient Conditions for Optimal Matching Parameters of Hilbert-Type Series Operator with a Class of Non-Homogeneous Kernel

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:lp^(α(a,b))→lp^(β(a,b))的算子范数,针对非齐次核K(m,n)=G(m^(λ)1/n^(λ)2(λ_(1)λ_(2)>0),利用权函数方法讨论算子T的最佳搭配参数a,b的充分必要条件,并在a,b为最佳搭配参数时,得到了T的算子范数表达式.

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:lp^(α(a,b))→lp^(β(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(m^(λ)1/n^(λ)2)(λ_(1)λ_(2)>0),and obtaied the norm formula of operator T when a and b are the best matching parameters.