A New Multiple Hilbert-Type Integral Inequality With A Non-Homogeneous Form

Source abstract

Hilbert-type inequalities are important in analysis and its applications. In recent years, some authors have studied and published a few Hilbert-type multiple integral inequalities, which are hard and interesting. In this paper, by estimating the weight function and technique of real analysis, the authors give a new multiple Hilbert-type integral inequality with a non-Homogeneous form as, F(x,y) f(x)g(y)dxdy < K f g (p >1). The best possible p,w q,w Rn+ x Rn+ constant factor is given, and the equivalent form is also considered. Many particular cases of Hilbert-type integral inequality with a non-homogeneous form are included. As its applications, the authors have considered some particular results.