On a new Hilbert-type integral inequality involving the upper limit functions

[摘要] By applying the weight functions and the idea of introduced parameters we give a new Hilbert-type integral inequality involving the upper limit functions and the beta and gamma functions. We consider equivalent statements of the best possible constant factor related to a few parameters. As applications, we obtain a corollary in the case of a nonhomogeneous kernel and some particular inequalities.

[学科分类] 电力

[关键词] Weight function;Hilbert-type integral inequality;Upper limit function;Parameter;Beta function;Gamma function