The Hilbert-Type Integral Inequalities with a Homogeneous Kernel of -Degree

A Hilbert-Type Integral Inequality in the Whole Plane with the Homogeneous Kernel of Degree -2

Multidimensional Hilbert-Type Inequalities with a Homogeneous Kernel

We consider the Hilbert-type inequalities with nonconjugate parameters. The obtaining of the best possible constants in the case of nonconjugate parameters remains still open. Our generalization will include a general homogeneous kernel. Also, we obtain the best possible constants in the case of conjugate parameters when the parameters satisfy appropriate conditions. We also compare our results...

On a Hardy-Hilbert-Type Inequality with a General Homogeneous Kernel

By the method of weight coefficients and techniques of real analysis, a Hardy-Hilbert-type inequality with a general homogeneous kernel and a best possible constant factor is given. The equivalent forms, the operator expressions with the norm, the reverses and some particular examples are also considered.

An extended multidimensional Hardy-Hilbert-type inequality with a general homogeneous kernel

In this paper, by the use of the weight coefficients, the transfer formula and the technique of real analysis, an extended multidimensional Hardy-Hilbert-type inequality with a general homogeneous kernel and a best possible constant factor is given. Moreover, the equivalent forms, the operator expressions and a few examples are considered.

Hardy-Hilbert-Type Inequalities with a Homogeneous Kernel in Discrete Case

Hilbert and Hardy-Hilbert type inequalities see 1 are very significant weight inequalities which play an important role in many fields of mathematics. Although classical, such inequalities have attracted the interest of numerous mathematicians and have been generalized in many different ways. Also the numerous mathematicians reproved them using various techniques. Some possibilities of generali...