engleski

A unified treatment of half-discrete Hilbert-type inequalities with a homogeneous kernel

In this paper we provide a unified treatment of half-discrete Hilbert-type inequalities with a general homogeneous kernel. The main results are proved for the case of non-conjugate exponents. A special emphasis is given to determining conditions under which these inequalities include the best possible constants. As an application, we consider some operator expressions closely connected to established inequalities. Finally, we also provide improvements of derived half-discrete inequalities by virtue of the Hermite-Hadamard inequality.

half-discrete inequality; Hilbert-type inequality; Hardy-Hilbert-type inequality; homogeneous kernel; the best constant; non-conjugate exponents; Beta function

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