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On Hilbert type inequalities with non-conjugate parameters. (English) Zbl 1167.26315
Different versions of the Hilbert inequality has been investigated by many mathematicians, see [A. Kufner, L. Maligranda and L.-E. Persson, The Hardy inequality. About its history and some related results, Pilsen: Vydavatelský Servis (2007; Zbl 1213.42001)]. Utilizing the properties of rearrangement of a function, the authors present some Hilbert type inequalities with non-conjugate parameters and by using a new analytic technique they find the best possible constants in these inequalities.
MSC:
26D10Inequalities involving derivatives, differential and integral operators
26D15Inequalities for sums, series and integrals of real functions
46E30Spaces of measurable functions
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