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Weight characterizations of discrete Hardy and Carleman type inequalities
2005 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis deals with some generalizations of the discrete Hardy and Carleman type inequalities and the relations between them. In Chapter 1 we give an introduction and overview of the area that serves as a frame for the rest of the thesis. In particular, a fairly complete description of the development of discrete Hardy and Carleman type inequalities in one and more dimensions can be found in this chapter. In Chapter 2 we consider some scales of weight characterizations for the one-dimensional discrete Hardy inequality for the case 1In Chapter 3 we present and discuss a new scale of weight characterizations for a two-dimensional discrete Hardy type inequality and its limit two-dimensional Carleman type inequality. In Chapter 4 we generalize the work done in Chapters 2 and 3 and present, prove and discuss the corresponding general n-dimensional versions. In Chapter 5 we introduce the study of the general Hardy type inequality with kernels involved. For kernels of product type a weight characterization is given, thus generalizing a previous result of M. Goldman. A scale of sufficient conditions is proved for the general case. Finally, in the Appendix some steps in the historical development of the continuous Hardy inequality are briefly described.

Place, publisher, year, edition, pages
Luleå: Luleå tekniska universitet, 2005. , p. 81
Series
Licentiate thesis / Luleå University of Technology, ISSN 1402-1757 ; 2005:45
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-26367Local ID: defcbd40-8e8d-11db-8975-000ea68e967bOAI: oai:DiVA.org:ltu-26367DiVA, id: diva2:999529
Note
Godkänd; 2005; 20061218 (haneit)Available from: 2016-09-30 Created: 2016-09-30 Last updated: 2017-11-24Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
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  • Other style
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Language
  • de-DE
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  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
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  • Other locale
More languages
Output format
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