Adiyasuren, Vandanjav; Batbold, Tserendorj; Krnić, Mario Hilbert-type inequalities involving differential operators, the best constants, and applications. (English) Zbl 1307.26018 Math. Inequal. Appl. 18, No. 1, 111-124 (2015). 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. Cited in 36 Documents MSC: 26D10 Inequalities involving derivatives and differential and integral operators 26D15 Inequalities for sums, series and integrals 33B15 Gamma, beta and polygamma functions Keywords:Hilbert-type inequality; Hardy inequality; differential operator; homogeneous function; gamma function PDFBibTeX XMLCite \textit{V. Adiyasuren} et al., Math. Inequal. Appl. 18, No. 1, 111--124 (2015; Zbl 1307.26018) Full Text: DOI