Hardy-type inequalities in fractional h-discrete calculus

Abstract

The first power weighted version of Hardy’s inequality can be rewritten asxα−1∫0x1tαf(t)dt)pdx≤[pp1]p∫0∞fp(x)dx,f≥0,p≥1,α < 1. In this paper we prove and discuss some discrete analogues of Hardy-type inequalities in fractional h-discrete calculus. Moreover, we prove that the corresponding constants are sharp.