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Using the way of weight functions and the technique of real analysis, a half-discrete Hilbert-type inequality with a general homogeneous kernel is obtained, and a best extension with two interval variables is given. The equivalent forms, the operator expressions, the reverses and some particular cases are considered.2000 Mathematics Subject Classification: 26D15; 47A07.

A half-discrete Hilbert-type inequality with a homogeneous kernel and an extension