engleski

On some multidimensional Hilbert-type inequalities in a discrete case

Motivated by results of Huang, in this paper we derive a pair of discrete multidimensional Hilbert-type inequalities involving homogeneous kernel of negative degree. 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 generalizations of some actual results, known from the literature.

Hilbert's inequality; homogeneous kernel; the best possible constant; conjugate exponents

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