A three-parameter logarithmic generalization of the Hilbert integral inequality

This is the authors' abstract. We don't add key points for this paper.

In this paper, we establish a new generalized form of the Hilbert integral inequality involving threeadjustable parameters and a logarithmic term. We prove that the resulting constant factor is sharp and best possible. Furthermore, we derive related forms of Hilbert-type integral inequalities, including those based on sharp lower bounds of the logarithmic function.