On the norm of an integral operator and applications

In this paper, the norm of an integral operator T : L r ( 0 , ∞ ) → L r ( 0 , ∞ ) ( r > 1 ) is obtained. As applications, a new bilinear integral operator inequality with the norm and the equivalent forms are given, and some new Hilbert's type inequalities with the best constant factors as the particular cases are established.