A HILBERT-TYPE INTEGRAL INEQUALITY IN THE FINITE INTERVAL

Abstract

In this paper, by using the methods of real analysis and functional analysis, a Hilbert-type integral inequality in the finite interval (0,b) (0 < b < \infty) with the homogeneous kernel of (-\lambda)-degree and a best constant factor is given. We also consider its operator expression. A few improved results, the equivalent forms and some new inequalities with the particular kernels are obtained.