New dynamic Hilbert-type inequalities in two independent variables involving Fenchel–Legendre transform

Abstract

Abstract In this paper, we establish some dynamic Hilbert-type inequalities in two independent variables on time scales by using the Fenchel–Legendre transform. We also apply our inequalities to discrete and continuous calculus to obtain some new inequalities as particular cases. Our results give more general forms of several previously established inequalities.

Keywords

• Hilbert’s inequality
• Dynamic inequality
• Time scales
• Fenchel–Young inequality