Naslov
On the norm of a multidimensional Hilbert-type operator

Autori
Bicheng, Yang ; Krnić, Mario

Izvornik
Sarajevo journal of mathematics (1840-0655) 7 (2011), 2; 223-243

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

Ključne riječi
Hilbert-type inequality; Hardy-Hilbert type inequality; multi\-dimensional Hilbert-type operator; homogeneous kernel; weight function; Beta function; Gamma function; norm.

Sažetak
In this paper we consider multidimensional Hilbert-type integral inequa\-lities with non-conjugate exponents and homogeneous kernels of negative degree. As an application, we define related Hilbert-type integral operators and consider their norms. The problem of determining the norm of such operators is equivalent to the problem of the best possible constant factors involved in the right-hand sides of related inequalities. In such a way, we obtain the norms and the best possible constant factors in some general settings with conjugate exponents. In particular, we obtain generalizations of some recent results, from the literature.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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