设λ1λ2≠0,若t>0时,K(x,y)满足K(tx,y)=K(x,tλ1/λ2y), K(x,ty)=K(tλ2/λ1x,y).则称K(x,y)是具有参数λ1和λ2的变量可转移函数,这是一种非齐次函数.该文研究了含λ1λ2<0情形的变量可转移函数核的Hilbert型级数不等式,并讨论其等价形式和最佳常数问题.
If λ1λ2 ≠ 0,t 〉 0,K(tx,y)=K(x,t λ1/λ2 y),K(x,ty) =K(t λ2/λ1 x,y).Then K(x,y) is called transferable variable function with parameters λ1 and λ2.In this paper,let λ1λ2 〈 0,Hilbert type series inequality with transferable variable kernel is studied.The equivalent form and the best constant factor are considered.