A Hardy-type inequality in two dimensions

On a decomposition of Hardy--Hilbert's type inequality

In this paper, two pairs of new inequalities are given, which decompose two Hilbert-type inequalities.

A Hardy-Hilbert Type Inequality

On a strengthened Hardy-Hilbert’s type inequality

In this paper, by using the Euler-Maclaurin expansion for the zeta function and estimating the weight function effectively, we derive a strengthenment of a Hardy-Hilbert’s type inequality proved by W.Y. Zhong. As applications, some particular results are considered.

A new restructured Hardy-Littlewood's inequality

In this paper, we reconstruct the Hardy-Littlewood’s inequality byusing the method of the weight coefficient and the technic of real analysis includinga best constant factor. An open problem is raised.

A Reverse Hardy-hilbert-type Integral Inequality

By estimating a weight function, a reverse Hardy-Hilbert-type integral inequality with a best constant factor is obtained. As an application, some equivalent forms and some particular results have been established.