Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • 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
Forever Young: Convolution Inequalities in Weighted Lorentz-type Spaces
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.ORCID iD: 0000-0003-0234-1645
2014 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis is devoted to an investigation of boundedness of a general convolution operator between certain weighted Lorentz-type spaces with the aim of proving analogues of the Young convolution inequality for these spaces.

Necessary and sufficient conditions on the kernel function are given, for which the convolution operator with the fixed kernel is bounded between a certain domain space and the weighted Lorentz space of type Gamma. The considered domain spaces are the weighted Lorentz-type spaces defined in terms of the nondecreasing rearrangement of a function, the maximal function or the difference of these two quantities.

In each case of the domain space, the corresponding Young-type convolution inequality is proved and the optimality of involved rearrangement-invariant spaces in shown.

Furthermore, covering of the previously existing results is also discussed and some properties of the new rearrangement-invariant function spaces obtained during the process are studied.

Place, publisher, year, edition, pages
Karlstad: Karlstads universitet, 2014. , 23 p.
Series
Karlstad University Studies, ISSN 1403-8099 ; 2014:21
Keyword [en]
Convolution, Young inequality, Lorentz spaces, weights, rearrangement-invariant spaces
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-31754ISBN: 978-91-7063-552-6 (print)OAI: oai:DiVA.org:kau-31754DiVA: diva2:706959
Presentation
2014-05-09, 3B426, Karlstads universitet, Universitetsgatan 2, Karlstad, 10:15 (English)
Opponent
Supervisors
Note

Paper II was a manuscript at the time of the defense.

Available from: 2014-04-17 Created: 2014-03-24 Last updated: 2017-12-06Bibliographically approved
List of papers
1. Convolution inequalities in weighted Lorentz spaces
Open this publication in new window or tab >>Convolution inequalities in weighted Lorentz spaces
2014 (English)In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 17, no 4, 1201-1223 p.Article in journal (Refereed) Published
Abstract [en]

We characterize boundedness of a convolution operator with a fixed kernel between the weighted Lorentz spaces Lambda(p)(v) and Gamma(q)(w) for 0 < p <= q <= infinity, 1 <= q < p < infinity and 0 < q <= p = infinity. We provide corresponding weighted Young-type inequalities and also study basic properties of some new involved r.i. spaces.

Place, publisher, year, edition, pages
Croatia: Element, 2014
Keyword
Convolution, Young inequality, O’Neil inequality, Lorentz spaces, weights
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-31751 (URN)10.7153/mia-17-90 (DOI)000345462600001 ()
Available from: 2014-03-23 Created: 2014-03-23 Last updated: 2017-12-06Bibliographically approved
2. Convolution in Rearrangement-Invariant Spaces Defined in Terms of Oscillation and the Maximal Function
Open this publication in new window or tab >>Convolution in Rearrangement-Invariant Spaces Defined in Terms of Oscillation and the Maximal Function
2014 (English)In: Zeitschrift für Analysis und ihre Anwendungen, ISSN 0232-2064, E-ISSN 1661-4534, Vol. 33, no 4, 369-383 p.Article in journal (Refereed) Published
Abstract [en]

We characterize boundedness of a convolution operator with a fixed kernel between the classes S p ( v), de fined in terms of oscillation, and weighted Lorentz spaces Gamma(q)(w), defined in terms of the maximal function, for 0 < p; q <= infinity. We prove corresponding weighted Young-type inequalities of the form parallel to f * g parallel to Gamma(q)(w) <= C parallel to f parallel to S-p(v)parallel to g parallel to Y and characterize the optimal rearrangement-invariant space Y for which these inequalities hold.

Keyword
Convolution, Young inequality, weighted Lorentz spaces, oscillation
National Category
Mathematics
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-41570 (URN)10.4171/ZAA/1517 (DOI)000347639000001 ()
Available from: 2016-04-22 Created: 2016-04-11 Last updated: 2017-11-30Bibliographically approved
3. Convolution in weighted Lorentz spaces of type Γ
Open this publication in new window or tab >>Convolution in weighted Lorentz spaces of type Γ
2016 (English)In: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 119, no 1, 113-132 p.Article in journal (Refereed) Published
Place, publisher, year, edition, pages
Aarhus Universitetsforlag, 2016
Keyword
Convolution, Young inequality, Lorentz spaces, weights
National Category
Mathematical Analysis
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-31752 (URN)10.7146/math.scand.a-24187 (DOI)000383815600007 ()
Note

This article was published as manuscript in Martin Křepelas licentiate thesis.

Available from: 2014-03-23 Created: 2014-03-23 Last updated: 2017-12-06Bibliographically approved

Open Access in DiVA

Forever Young(1159 kB)383 downloads
File information
File name FULLTEXT01.pdfFile size 1159 kBChecksum SHA-512
edc64fd90bd0801de44e40bea97784a6af398124bb2458ed7139a89be00fa4bae7b20ff62e03ba6ccbef69ed7e3014b3f71e4b43b0a59c0bdd0f7149341353f1
Type fulltextMimetype application/pdf

Search in DiVA

By author/editor
Křepela, Martin
By organisation
Department of Mathematics and Computer Science
Mathematical Analysis

Search outside of DiVA

GoogleGoogle Scholar
Total: 383 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

isbn
urn-nbn

Altmetric score

isbn
urn-nbn
Total: 421 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • 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