engleski

Half-discrete Hilbert-type inequalities with mean operators, the best constants, and applications

In this article we derive several new half-discrete Hilbert-type inequalities with a general homogeneous kernel, involving arithmetic, geometric and harmonic mean operators. 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.

half-discrete Hilbert-type inequality; Hardy inequality; Carleman inequality; Knopp inequality; the best constant; arithmetic mean; geometric mean; harmonic mean

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