On a Best Extension of a Half-Discrete Hilbert-Type Inequality

Abstract

By using the way of weight functions and the technique of real analysis, a best extension of a half-discrete Hilbert-type inequality with one-pair conjugate exponents and two interval variables is given. The equivalent forms, the operator expressions and the reverses are considered.

Key words and phrases. Hilbert-type inequality, variable, weight function, equivalent form, reverse.

2000 Mathematics Subject Classification. 26D15, 47A07