On Hilbert's Inequality for Double Series and Its Applications

الملخص EN

This study shows that a refinement of the Hilbert inequality for double series can be established by introducing a real function u(x) and a parameter λ.

In particular, some sharp results of the classical Hilbert inequality are obtained by means of a sharpening of the Cauchy inequality.

As applications, some refinements of both the Fejer-Riesz inequality and Hardy inequality in Hp function are given.