Hilbert-type inequalities involving differential operators, the best constants, and applications

By V. Adiyasuren, Tserendorj Batbold, Mario Krnic. 2015

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Motivated by some recent results, in this article we derive several Hilbert-type inequalities with a differential operator, regarding a general homogeneous kernel. Moreover, we show that the constants appearing on the right-hand sides of these inequalities are the best possible. The general results are then applied to some particular examples of homogeneous kernels and compared with previously known from the literature. Mathematics subject classification (2010): Primary 26D10, 26D15, Secondary 33B15.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/e1ab96cad0ef725cc8f7d0006e441cf4cd931d01