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Some New Contributi...
Some New Contributions in the Theory of Hardy Type Inequalities
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- Yimer, Markos Fisseha, 1984- (author)
- Karlstads universitet,Institutionen för matematik och datavetenskap (from 2013)
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- Barza, Sorina, Professor, 1967- (thesis advisor)
- Karlstads universitet,Institutionen för matematik och datavetenskap (from 2013)
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- Persson, Lars-Erik, Professor (thesis advisor)
- Karlstads universitet,Institutionen för matematik och datavetenskap (from 2013)
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- Lind, Martin, Assoc. prof. 1985- (thesis advisor)
- Karlstads universitet,Institutionen för matematik och datavetenskap (from 2013)
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- Marcoci, Liviu-Gabriel, Assoc. prof. (thesis advisor)
- Technical University of Civil Engineering Bucharest, Romania
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- Pick, Lubos, Professor (opponent)
- Charles University of Prague, Czech Republic
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(creator_code:org_t)
- ISBN 9789178674022
- Karlstad : Karlstads universitet, 2023
- English 41 s.
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Series: Karlstad University Studies, 1403-8099 ; 2023:27
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Abstract
Subject headings
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- In this thesis we derive various generalizations and refinements of some classical inequalities in different function spaces. We consider some of the most important inequalities namely the Hardy, Pólya-Knopp, Jensen, Minkowski and Beckenbach-Dresher inequalities. The main focus is put on the Hardy and their limit Pólya-Knopp inequalities. Indeed, we derive such inequalities even in a general Banach functionsetting.The thesis consists of three papers (A, B and C) and an introduction, which put these papers into a more general frame. This introduction has also independent interest since it shortly describe the dramatic more than 100 years of development of Hardy-type inequalities. It contains both well-known and very new ideas and results.In paper A we prove and discuss some new Hardy-type inequalities in Banach function space settings. In particular, such a result is proved and applied for a new general Hardy operator, which is introduced in this paper (this operator generalizes the usualHardy kernel operator). These results generalize and unify several classical Hardy-type inequalities.In paper B we prove some new refined Hardy-type inequalities again in Banach function space settings. The used (super quadraticity) technique is also illustrated by making refinements of some generalized forms of the Jensen, Minkowski and Beckenbach-Dresher inequalities. These results both generalize and unify several results of this type.In paper C for the case 0
- In this thesis we derive various generalizations and refinements of some classical inequalities in different function spaces. We consider some of the most important inequalities namely the Hardy, Pólya-Knopp, Jensen, Minkowski and Beckenbach-Dresher inequalities. The main focus is put on the Hardy and their limit, Pólya-Knopp inequalities. Indeed, we derive such inequalities even in a general Banach function setting. We prove and discuss some new Hardy-type inequalities in Banach function space settings. In particular, such a result is proved and applied for a new general Hardy operator. These results generalize and unify several classical Hardy-type inequalities.Next, we prove some new refined Hardy-type inequalities again in Banach function space settings. We used superquadraticity technique to prove refinements of some classical inequalities.Finally, for the case 0
Subject headings
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Keyword
- integral inequalities
- Hardy-type inequalities
- Pólya-Knopp’s inequality
- Jensen’s inequality
- Minkowski’s inequality
- Beckenbach-Dresher’s inequality
- sharp constants
- measures
- superquadratic functions
- refinements
- Banach function spaces
- Matematik
- Mathematics
Publication and Content Type
- vet (subject category)
- lic (subject category)
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