Abstract:

A  Hilbert’s inequality of biparameter type was investigated by introducing the parameters: λ₁,λ₂, and using the way of weight coefficient and the method of real analysis. A Hilberttype integral inequality with several parameters and its equivalent form were obtained, and their constant factors were proved to be the optimum value.  A series of Hilbert’s type integral inequalities with more simple forms were obtained via selecting the appropriate parameters satisfying the conditions  selected in the results.

Key words: Hilberttype integral inequality, parameter, weight coefficient, the best constant factor, Hlder’s inequality, application