Naslov
On a strengthened multidimensional Hilbert-type inequality

Autori
Krnić, Mario

Izvornik
Mathematica slovaca (0139-9918) 64 (2014), 5; 1165-1182

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

Ključne riječi
Hilbert-type inequality; conjugate exponents; Holder's inequality; refinement; converse

Sažetak
The main objective of this paper is a study of the general refinement and converse of the multidimensional Hilbert-type inequality in the so-called quotient form. Such extensions are deduced with the help of the sophisticated use of the well-known Holder's inequality. The obtained results are then applied to homogeneous kernels with the negative degree of homogeneity. Also, we establish the conditions under which the constant factors involved in the established inequalities are the best possible. Finally, we consider some particular settings with homogeneous kernels and weighted functions. In such a way we obtain both refinements and converses of some actual results, known from the literature.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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