On Some Multidimensional Hilbert-Type Inequalities in the Discrete Case
Motivated by the results of Huang, we deduce a pair of discrete multidimensional Hilbert-type inequalities involving a homogeneous kernel of negative degree. We also establish conditions under which the constant factors involved in the established inequalities are the best possible. Finally, we consider some particular settings with homogeneous kernels and weight functions. In this way, we obtain generalizations of some results known from the literature.
English version (Springer): Ukrainian Mathematical Journal 65 (2013), no. 6, pp 891-903.
Citation Example: Krnić M., Vuković P. On Some Multidimensional Hilbert-Type Inequalities in the Discrete Case // Ukr. Mat. Zh. - 2013. - 65, № 6. - pp. 802–813.