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An extended Hilbert's integral inequality in the whole plane with parameters
Leping He1, Yin Li1, Bicheng Yang2
11College of Mathematics and Statistics, Jishou University, Jishou, P.R. China.
Journal of Inequalities and Applications
|March 7, 2019
Abstract:
By introducing independent parameters and interval variables, applying the weight functions and the technique of real analysis, an extended Hilbert's integral inequality in the whole plane with parameters and a best possible constant factor is provided. The equivalent forms, the reverses, and the related homogeneous forms with particular parameters are considered. Meanwhile, an extended Hilbert's integral operator in the whole plane is defined, and the operator expressions for the equivalent inequalities are obtained.