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On the multidimensional Hilbert-type inequalities involving the hardy operator

Krnić Mario (Faculty of Electrical Engineering and Computing, Zagreb, Croatia)

This paper deals with the multidimensional Hilbert-type inequalities involving the Hardy operator and homogeneous kernels. The main results are established in the setting with the non-conjugate exponents. After reduction to the conjugate case, the inequalities with the best possible constant factors are obtained in some general cases. As an application, some particular settings are considered in order to obtain the multidimensional extensions of some recent results, known from the literature.

Keywords: Hilbert inequality, Hardy inequality, Hardy operator, conjugate exponents, on-conjugate exponents, best possible constant factors