Hilbert-type inequalities involving differential operators, the best constants, and applications
Vandanjav Adiyasuren, Tserendorj Batbold, Mario Krnić · Mathematical Inequalities & Applications · 2014
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.