Equivalent property of a half-discrete Hilbert’s inequality with parameters

Abstract

Abstract By using the weight functions and the idea of introducing parameters, a half-discrete Hilbert inequality with a nonhomogeneous kernel and its equivalent form are given. The equivalent statements of the constant factor are best possible related to parameters, and some particular cases are considered. The cases of a homogeneous kernel are also deduced.

Keywords

• Weight function
• Half-discrete Hilbert’s inequality
• Equivalent form
• Best possible constant factor