一类准齐次核的Hilbert型级数不等式成立的充要条件及应用

摘要

Let a nonnegative function K(x ,y) satisfy the condition :when t>0 ,there were K(tx,y)=tλλ1K(x,t-λ1/λ2y),K(x,ty)=tλλ2K(t-λ2/λ1x,y).By using real analysis techinques and the method of weight functions, we gave the necessary and sufficient condition for the establishment of Hilbert-type series inequalities with this quasihomogeneous kernel K （m,n） and the best constant factors, and discussed its applications in the operator theory.%设非负函数K(x,y)满足条件:当t>0时,有K(tx,y)=tλλ1K(x,t-λ1/λ2y),K(x,ty)=tλλ2K(t-λ2/λ1x,y).利用实分析技巧及权函数方法,给出具有这类准齐次核K(m,n)的Hilbert型级数不等式成立的充要条件和最佳常数因子,并讨论其在算子理论中的应用.