A general logarithmic-Hardy-Hilbert integral inequality

Abstract This article presents a modified version of the Hardy-Hilbert integral inequality. It takes the form of a generalized logarithmic-Hardy-Hilbert inequality with four adjustable parameters. These parameters allow for a wide range of special cases. Several known results are recovered and new ones are derived. We present inequalities with explicit, tractable upper bounds. These involve weighted integral norms with power-weight functions. Full proofs are included to make the article self-contained.