INEQUALITIES OF THE HILBERT TYPE IN $\mathbb{R}^{n}$ WITH NON-CONJUGATE EXPONENTS
INEQUALITIES OF THE HILBERT TYPE IN $\mathbb{R}^{n}$ WITH NON-CONJUGATE EXPONENTS
Abstract In this paper we state and prove a new general Hilbert-type inequality in $\mathbb{R}^{n}$ with $k\geq2$ non-conjugate exponents. Using Selberg's integral formula, this result is then applied to obtain explicit upper bounds for the doubly weighted Hardy–Littlewood–Sobolev inequality and some further Hilbert-type inequalities for $k$ non-negative functions and non-conjugate …