An Equivalent Form Related to a Hilbert-Type Integral Inequality

A new Hilbert-type integral inequality and the equivalent form

We give a new Hilbert-type integral inequality with the best constant factor by estimating the weight function. And the equivalent form is considered.

A Hilbert Integral-Type Inequality with Parameters

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.

A multidimensional discrete Hilbert-type inequality

In this paper, by using the way of weight coecients and technique of real analysis, a multidimensionaldiscrete Hilbert-type inequality with a best possible constant factor is given. The equivalentform, the operator expression with the norm are considered.

Equivalent Conditions of a Hardy-type Integral Inequality Related to the Extended Riemann Zeta Function

Abstract. By the use of techniques of real analysis and weight functions, we obtain two lemmas and build a few equivalent conditions of a Hardy-type integral inequality with a non-homogeneous kernel, related to a parameter where the constant factor is expressed in terms of the extended Riemann zeta function. Meanwhile, a few equivalent conditions for two kinds of Hardytype integral inequalities...