engleski

On some refinements and converses of multidimensional Hilbert-type inequalities

The main objective of this paper is a study of some new refinements and converses of multidimensional Hilbert-type inequalities with non-conjugate exponents. Such extensions are deduced with the help of some remarkable improvements of the well-known H\"{; ; ; o}; ; ; lder's inequality. First, we obtain refinements and converses of the general multidimensional Hilbert-type inequality in both quotient and difference form. The obtained results are then applied to homogeneous kernels with the negative degree of homogeneity. Finally, we consider some particular settings with homogeneous kernels and weighted functions, and compare our results with the previously known from the literature.

Hilbert-type inequality ; non-conjugate exponents

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