Dynamic Hardy-type inequalities with non-conjugate parameters

Abstract

Within this paper, we derive entire series of new Hilbert and Hardy-Hilbert form integral inequalities with non-conjugate exponents on time scales. Firstly, we demonstrate and discuss two general equivalent inequalities of this type, as well as their corresponding reverse inequalities. We also extend Hilbert and Hardy-Hilbert inequalities in their most general form. The results obtained are then applied to a kernel of special Hardy form. Our results as special cases extend some of the dynamic inequalities achieved on time scales and also include some integral inequalities as special cases when T=R.

Keywords

• 26D10
• 26D15
• 46G12
• 47B34
• 47J20
• 28A25