ON THE NORM OF A CERTAIN SELF-ADJOINT INTEGRAL OPERATOR AND APPLICATIONS TO BILINEAR INTEGRAL INEQUALITIES

Abstract

In this paper, the norm of a bounded self-adjoint integral operator $T:$ $% L^{2}(0,\infty )\rightarrow L^{2}(0,\infty )$ is obtained. As applications, a new bilinear integral inequality with a best constant factor and some particular cases such as Hilbert- type inequalities are considered.