Abstract:

Supposing that 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. When λ₁λ₂<0, Hilbert’s type integral inequality with the kernel of transferable variable function was studied  via the technique of real analysis, and the best constant factor was discussed.

Key words: transferable variable function, Hilbert’s type integral inequality, the best constant factor