Abstract: Firstly, the concept of quasi-homogeneous kernel was introduced to discuss Hilbert-type integral inequalities with quasi-homogeneous kernel in weighted Lebesgue spaces with exponential functions. Secondly, by using the weight coefficient method and several  analysis techniques, equivalent parameter condition for optimal Hilbert-type integral inequalities was given, and the calculation formula for the best constant factor was obtained. Finally, its applications in operator theory were discussed.

Key words:  , weighted Lebesgue space, quasi-homogeneous kernel, Hilbert-type integral inequality, optimal matching parameter, equivalent condition, bounded operator, operator norm