A Hilbert-type integral inequality with a hybrid kernel and its applications
Volume 143 / 2016
Colloquium Mathematicum 143 (2016), 193-207 MSC: Primary 26D15. DOI: 10.4064/cm6572-1-2016 Published online: 4 January 2016
We prove a multi-parameter Hilbert-type integral inequality with a hybrid kernel. We describe the best constant in the inequality in terms of hypergeometric functions. Some equivalent forms of the inequalities are also studied. By specifying parameter values we obtain results proved by other authors as well as many new inequalities.