A Hilbert-Type Integral Inequality in the Whole Plane with the Homogeneous Kernel of Degree −2

Abstract

By applying the way of real and complex analysis and estimating the weight functions, we build a new Hilbert-type integral inequality in the whole plane with the homogeneous kernel of degree −2 involving some parameters and the best constant factor. We also consider its reverse. The equivalent forms and some particular cases are obtained.