Hardy-type inequalities in fractional h-discrete calculus

Abstract

The first power weighted version of Hardy’s inequality can be rewritten as [<i>mathematical formula</i>] where the constant <i>C</i> =[<i>p</i> / <i>p</i> - <i><b>a</b></i> - 1]^<i>p</i> is sharp. This inequality holds in the reversed direction when<math xmlns="http://www.w3.org/1998/Math/MathML"> <mn>0</mn> <mo>&#x2264;<!-- ≤ --></mo> <mi><i>p</i></mi> <mo>&lt;</mo> <mn>1</mn> </math>. 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. Keywords