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On Hardy q-inequalities
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.ORCID iD: 0000-0002-9584-4083
L.N. Gumilyov Eurasian National University.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
2014 (English)In: Czechoslovak Mathematical Journal, ISSN 0011-4642, E-ISSN 1572-9141, Vol. 64, no 3, 659-682 p.Article in journal (Refereed) Published
Abstract [en]

Some $q$-analysis variants of Hardy type inequalities of the form \int_0^b \bigg(x^{\alpha-1} \int_0^x t^{-\alpha} f(t) d_q t \bigg)^{\!p} d_q x \leq C \int_0^b f^p(t) d_q t with sharp constant $C$ are proved and discussed. A similar result with the Riemann-Liouville operator involved is also proved. Finally, it is pointed out that by using these techniques we can also obtain some new discrete Hardy and Copson type inequalities in the classical case.

Place, publisher, year, edition, pages
2014. Vol. 64, no 3, 659-682 p.
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-6106Local ID: 44f1c2c8-afc2-407d-9cac-7c1a440b757eOAI: oai:DiVA.org:ltu-6106DiVA: diva2:978983
Note
Validerad; 2014; 20141215 (ysko)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved

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