engleski

Discrete Hilbert-type inequalities with general homogeneous kernels

The main objective of this paper is an unified treatment of discrete Hilbert-type inequalities with homogeneous kernels. At the beginning, we prove and discuss two equivalent general inequalities of such type. Further, we analyze the conditions which yield the best possible constant factors in obtained inequalities. The obtained results are then applied to various settings considering homogeneous functions of a negative real degree. In such a way, we obtain the generalizations of numerous results, previously known from the literature.

Hilbert-type inequality; Hardy-Hilbert type inequality; homogeneous kernel; the best possible constant; conjugate exponents; Beta function

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