engleski

Hardy-Hilbert type inequalities with fractional kernel in ${; ; ; \bf R}; ; ; ^n$

The main objective of this paper is some new special Hilbert-type and Hardy-Hilbert-type inequalities in ${; ; \bf (R^n)^k}; ; $ with $k\geq 2$ non-conjugate parameters which are obtained by using the well known Selberg's integral formula in appropriate form. In such a way we obtain extensions over the whole set of real numbers, of some earlier results, previously known from the literature, where the integrals were taken only over the set of positive real numbers. Also, we obtain the best possible constants in the conjugate case.

Inequalities; multiple Hilbert's inequality; multiple Hardy-Hilbert's inequality; equivalent inequalities; non-conjugate parameters; gamma function; Selberg's integral; the best possible constant; hypergeometric function

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