On a Hilbert-type integral inequality in the subinterval and its operatorexpression

Abstract

In this paper, by using the methods of real analysis and functional analysis, a Hilbert-type integral inequality in the subinterval $(a,\infty )\,\,(a>0)$ with the homogeneous kernel of $-\lambda $-degree and a best constant factor and its operator expression are given. As applications, a few improved results, the equivalent forms and some new inequalities with the particular kernels are obtained.