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Boundedness and compactness of a class of Hardy type operators
(Journal article; Tidsskriftartikkel; Peer reviewed, 2016-12-13)
We establish characterizations of both boundedness and of compactness of a general class of fractional integral operators involving the Riemann-Liouville, Hadamard, and Erdelyi-Kober operators. In particular, these results imply new results in the theory of Hardy type inequalities. As applications both new and well-known results are pointed out.
Hardy-type inequalities in fractional h-discrete calculus
(Journal article; Tidsskriftartikkel; Peer reviewed, 2018-04-04)
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]<sup><i>p</i></sup> is sharp. This inequality holds in the reversed direction when<math xmlns="http://www.w3.org/1998/Math/MathML"> <mn>0</mn> <mo>≤<!-- ≤ --></mo> <mi><i>p</i></mi> <mo><</mo> <mn>1</mn> ...