A Hilbert-type integral inequality in the whole plane related to the kernel of exponent function

Abstract

Abstract By using real analysis and weight functions, we obtain a few equivalent statements of a Hilbert-type integral inequality in the whole plane related to the kernel of exponent function with intermediate variables. The constant factor related to the gamma function is proved to be the best possible. We also consider some particular cases and the operator expressions.

Keywords

• Hilbert-type integral inequality
• Weight function
• Intermediate variable
• Equivalent statement
• Operator
• Gamma function