Some sharp inequalities for multidimensional integral operators with homogeneous kernel: an overview and new results

Lukkassen, D.; Persson, L. E.; Samko, Stefan; Wall, P.

http://hdl.handle.net/10400.1/9544

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Abstract(s)

One 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.