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Title: On Hardy $q$-inequalities (English)
Author: Maligranda, Lech
Author: Oinarov, Ryskul
Author: Persson, Lars-Erik
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 64
Issue: 3
Year: 2014
Pages: 659-682
Summary lang: English
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Category: math
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Summary: Some $q$-analysis variants of Hardy type inequalities of the form $$ \int _0^b \bigg (x^{\alpha -1} \int _0^x t^{-\alpha } f(t) {\rm d}_q t \bigg )^{p} {\rm d}_q x \leq C \int _0^b f^p(t) {\rm d}_q t $$ 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. (English)
Keyword: inequality
Keyword: Hardy type inequality
Keyword: Hardy operator
Keyword: Riemann-Liouville operator
Keyword: $q$-analysis
Keyword: sharp constant
Keyword: discrete Hardy type inequality
MSC: 26D10
MSC: 26D15
MSC: 39A13
idZBL: Zbl 06391518
idMR: MR3298553
DOI: 10.1007/s10587-014-0125-6
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Date available: 2014-12-19T16:01:54Z
Last updated: 2016-10-03
Stable URL: http://hdl.handle.net/10338.dmlcz/144051
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