×

Hilbert-type inequalities involving differential operators, the best constants, and applications. (English) Zbl 1307.26018

Summary: 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.

MSC:

26D10 Inequalities involving derivatives and differential and integral operators
26D15 Inequalities for sums, series and integrals
33B15 Gamma, beta and polygamma functions
PDFBibTeX XMLCite
Full Text: DOI