又一类具有准齐次核的 Hilbert 型积分不等式

摘要

Supposing that t>0,λ1λ2 ≠0,if function K (x ,y )satisfies:K (tx ,y )=tλ1 K (x ,t-λ1/λ2 y ), K (x ,ty )=tλ2 K (t-λ2/λ1 x ,y ), then K (x ,y )is called quasi-homogeneous funtion of order (λ1 ,λ2 ).In this paper,a new Hilbert’s type integral inequality with a quasi-homogeneous kernel of λ1λ2 < 0 was studied by the weight function,with its best constant factor discussed.%设 t>0,λ1λ2≠0,若函数 K (x ,y )满足K (tx ,y )=tλ1 K (x ,t-λ1/λ2 y ), K (x ,ty )=tλ2 K (t-λ2/λ1 x ,y ),则称 K (x ,y )是(λ1,λ2)阶的准齐次函数。利用权函数方法,考虑λ1λ2<0情形下具有这种准齐次积分核的 Hilbert 型积分不等式,并讨论其最佳常数问题。