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Hardy-type inequalities in fractional h-discrete calculus
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UiT The Artic University of Norway, Narvik, Norway.
L. N. Gumilyev Eurasian National University, Astana, Kazakhstan.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. L. N. Gumilyev Eurasian National University, Astana, Kazakhstan.
2018 (English)In: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, no 1, article id 73Article in journal (Refereed) Published
Abstract [en]

The first power weighted version of Hardy’s inequality can be rewritten as∫∞0(xα−1∫x01tαf(t)dt)pdx≤[pp−α−1]p∫∞0fp(x)dx,f≥0,p≥1,α<p−1,where the constant C=[pp−α−1]p is sharp. This inequality holds in the reversed direction when 0≤p<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.

Place, publisher, year, edition, pages
Springer, 2018. no 1, article id 73
Keywords [en]
Inequality, Integral operator, h-calculus, h-integral, Discrete Fractional Calculus
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-68169DOI: 10.1186/s13660-018-1662-6ISI: 000429238300001PubMedID: 29628749Scopus ID: 2-s2.0-85045115925OAI: oai:DiVA.org:ltu-68169DiVA, id: diva2:1195193
Note

Validerad;2018;Nivå 2;2018-04-04 (rokbeg)

Available from: 2018-04-04 Created: 2018-04-04 Last updated: 2019-03-04Bibliographically approved
In thesis
1. Hardy-type inequalities in quantum calculus
Open this publication in new window or tab >>Hardy-type inequalities in quantum calculus
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Alternative title[sv]
Hardy-typ olikheter i q-analys
Place, publisher, year, edition, pages
Luleå: Luleå University of Technology, 2018
Series
Doctoral thesis / Luleå University of Technology 1 jan 1997 → …, ISSN 1402-1544
National Category
Mathematics Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-71319 (URN)978-91-7790-240-9 (ISBN)978-91-7790-241-6 (ISBN)
Public defence
2018-12-10, E246, Luleå, 10:00 (English)
Opponent
Supervisors
Available from: 2018-10-24 Created: 2018-10-24 Last updated: 2019-03-04Bibliographically approved

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