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A Unified Treatment of Half-Discrete Hilbert-Type Inequalities with a Homogeneous Kernel |
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| Authors: | Mario Krnić Josip Pečarić Predrag Vuković |
| Institution: | 1. University of Zagreb, Faculty of Electrical Engineering and Computing, Unska 3, 10000, Zagreb, Croatia 2. University of Zagreb, Faculty of Textile Technology, Pierottijeva 6, 10000, Zagreb, Croatia 3. University of Zagreb, Faculty of Teacher Education, Savska cesta 77, 10000, Zagreb, Croatia |
| Abstract: | 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. |
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