engleski

On some higher-dimensional Hilbert's and Hardy-Hilbert's integral inequalities with parameters

By introducing some parameters and a norm |x|_\alpha, x\in {; ; ; ; R_+}; ; ; ; ^n, we give higher-dimensional Hilbert's and Hardy-Hilbert's integral inequalities in non-conjugate case. Further, we prove that their constant factors are the best possible, in the conjugate case, when the parameters satisfy appropriate conditions. We also compare our results with some known results.

Inequalities; Beta function; Gamma function; Hilbert's inequality; Hardy-Hilbert's inequality; conjugate exponents; non-conjugate exponents; the best possible constant

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