Lukkassen, D.Persson, L. E.Samko, StefanWall, P.2017-04-072017-04-072016-041331-4343http://hdl.handle.net/10400.1/9544One goal of this paper is to point out the fact that a big number of inequalities proved from time to time in journal publications, both one-dimensional and multi-dimensional, are particular cases of some general results for integral operators with homogeneous kernels, including in particular, the statements on sharp constants.Some new multidimensional Hardy-Hilbert type inequalities are derived. Moreover, a new multidimensional Polya-Knopp inequality is proved and some examples of applications are derived from this result. The constants in all inequalities are sharp.engMultidimensional inequalitiesHardy-Hilbert type inequalitiesP ´olya-Knopp type inequalitiesSharp constantsjournal article10.7153/mia-19-41