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

Autori
Krnić, Mario ; Pečarić, Josip ; Perić, Ivan ; Vuković, Predrag

Izvornik
Journal of inequalities in pure and applied mathematics (1443-5756) 10 (2009), 4; 115-1

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
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

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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