engleski

Inequalities of the Hilbert type in R^n with non-conjugate exponents

In this paper we state and prove a new general Hilbert-type inequality in R^n with k>=2 non-conjugate exponents. Using Selberg's integral formula, this resuly is then applied to obtain explicit upper bounds for the doubly weighted Hardy-Littlewood-Sobolev inequality and some further Hilbert-type inequaliyies for k non-negative functions and non-conjugate exponents.

Inequalities; Hilbert's inequality; doubly weighted Hardy-Littlewood-Sobolev inequality; Selberg's integral formula; Gamma function; Beta function

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