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Optimal relationships between L-p-norms for the Hardy operator and its dual
Karlstad University, Faculty of Technology and Science, Department of Mathematics.ORCID iD: 0000-0001-5459-0796
2014 (English)In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 193, no 2, p. 423-430Article in journal (Refereed) Published
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Abstract [en]

We obtain sharp two-sided inequalities between -norms of functions and , where is the Hardy operator, is its dual, and is a nonnegative measurable function on In an equivalent form, it gives sharp constants in the two-sided relationships between -norms of functions and , where is a nonnegative nonincreasing function on with In particular, it provides an alternative proof of a result obtained by Kruglyak and Setterqvist (Proc Am Math Soc 136:2005-2013, 2008) for and by Boza and Soria (J Funct Anal 260:1020-1028, 2011) for all , and gives a sharp version of this result for 1 < p < 2.

Place, publisher, year, edition, pages
Springer, 2014. Vol. 193, no 2, p. 423-430
Keyword [en]
Hardy operator, Dual operator, Best constants
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-41542DOI: 10.1007/s10231-012-0283-9ISI: 000333199900007OAI: oai:DiVA.org:kau-41542DiVA, id: diva2:923114
Available from: 2016-04-25 Created: 2016-04-11 Last updated: 2017-11-30Bibliographically approved

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Kolyada, Viktor

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