Abstract:

Supposing that t>0, λ₁λ₂≠0, if function K(x,y) satisfies: K(tx,y)=t^λ1K(x,t^-λ1/λ2y),K(x,ty)=t^λ2K(t^-λ2/λ1x,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.

Key words:  quasi-homogeneous integral kernel, Hilbert’s type integral inequality, the best constant factor