On Hilbert's inequality for double series and its applications (Q938516)

Summary: 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 \(\lambda \). 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 \(H_{p}\) function are given.