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

摘要

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.