A Hilbert-type integral inequality under configuring free power and its applications

Abstract

Abstract By using the method of weight function, the technique of real analysis, and the theory of special functions, a multi-parameter Hilbert-type integral inequality and its equivalent form are established, and their constant factors are proved to be the best possible. The expressions of operator with norm are given. As an application, relevant results in the references and some new inequalities are obtained by assigning some parameter values.

Keywords

• Hilbert-type integral inequality
• Weight function
• Whittaker function
• Operator
• Application