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Some new Hardy-type inequalities on the cone of non-decreasing functions
2017 (English)Report (Other academic)
Place, publisher, year, edition, pages
Luleå: Luleå University of Technology, 2017. , p. 18
Series
Gula serien, ISSN 1400-4003
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-68315OAI: oai:DiVA.org:ltu-68315DiVA, id: diva2:1197206
Available from: 2018-04-12 Created: 2018-04-12 Last updated: 2018-04-12Bibliographically approved
In thesis
1. Some new Hardy-type inequalities on the cone of monotone functions
Open this publication in new window or tab >>Some new Hardy-type inequalities on the cone of monotone functions
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Alternative title[sv]
Några nya Hardy-typ olikheter på konen av monotona funktioner
Abstract [en]

This PhD thesis is devoted to the study weighted Hardy-type inequalitieswith quasilinear integral operators on the cone of monotone functions. Thethesis consists of six papers (papers A - F) and an introduction, which givesa brief review of the theory of Hardy-type inequalities and also serves to putthese papers into a more general frame.

In papers A, D and E we characterize some weighted Hardy-type inequal-ities on the cone of non-increasing functions. This problem is related to theboundedness of the Hardy-Littlewood maximal operator in weighted LorentzΓ - spaces. In papers D and E the case with integral operators defined byso called Oinarov’s kernels are treated. In all cases necessary and sufficientconditions are derived.

In paper B we solve the similar problem for the cone of quasi-concavefunctions (i.e. when the function f satisfy two monotonicity conditions,namely that f (t) is non-decreasing and f(t)t is non-increasing). Such functions are of great importance for interpolation theory, approximation theory and related areas in functional analysis. Also here complete characterizations are given in all cases.

Paper C is devoted to characterizing weighted Hardy-type inequalities with supremum operators on the cone of monotone functions. In particular, the study of the case with non-decreasing functions was initiated in this paper.

In paper F we focus only on the much less studied problem, namely to characterize Hardy-type inequalities on the cone of non-decreasing functions. A new reduction method is used in a crucial way. Some complete charac-terizations for all studied cases are discussed and proved. The investigations initiated in paper C are here developed to a more general theory, which cov-ers all studied operators. The obtained results are used to derive some new bilinear Hardy-type inequalities.

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
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-68294 (URN)978-91-7790-102-0 (ISBN)978-91-7790-103-7 (ISBN)
Public defence
2018-06-08, E 243, Luleå, 10:00 (English)
Opponent
Supervisors
Available from: 2018-04-11 Created: 2018-04-11 Last updated: 2018-05-31Bibliographically approved

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf