非齐次核逆向Hilbert型积分不等式的最佳搭配参数及算子表达式

Optimal Matching Parameters for Inverse Hilbert-Type IntegralInequality with Non-homogeneous Kernel and Operator Expression

利用权函数方法,在1/p+1/q=1(0<p<1,q<0)的条件下,讨论具有非齐次核K(x,y)=G(x^(λ1)y^(λ2))(λ_(1)λ_(2)>0)的逆向Hilbert型积分不等式:∫+∞0∫+∞0K(x,y)|f(x)||g(y)|dxdy≥M‖f‖_(p,α)‖g‖_(q,β),给出其最佳搭配参数的充分必要条件,并讨论其算子表达式.

Using the power function method,we discussed the inverse Hilbert-type integral inequality∫+∞0∫+∞0K(x,y)|f(x)||g(y)|dxdy≥M‖f‖_(p,α)‖g‖_(q,β)with non-homogeneous kernel K(x,y)=G(x^(λ1)y^(λ2))(λ_(1)λ_(2)>0)under the condition that 1/p+1/q=1(0<p<1,q<0),then gave the necessary and sufficient conditions of optimal matching parameters,and discussed its operator expression.