Change search
ReferencesLink to record
Permanent link

Direct link
Convolution inequalities in weighted Lorentz spaces
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
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. Vol. 17, no 4, 1201-1223 p.
Keyword [en]
Convolution, Young inequality, O’Neil inequality, Lorentz spaces, weights
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-31751DOI: 10.7153/mia-17-90ISI: 000345462600001OAI: oai:DiVA.org:kau-31751DiVA: diva2:706894
Available from: 2014-03-23 Created: 2014-03-23 Last updated: 2016-11-03Bibliographically approved
In thesis
1. Forever Young: Convolution Inequalities in Weighted Lorentz-type Spaces
Open this publication in new window or tab >>Forever Young: Convolution Inequalities in Weighted Lorentz-type Spaces
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
Convolution, Young inequality, Lorentz spaces, weights, rearrangement-invariant spaces
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-31754 (URN)978-91-7063-552-6 (ISBN)
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: 2016-08-17Bibliographically approved
2.
The record could not be found. The reason may be that the record is no longer available or you may have typed in a wrong id in the address field.

Open Access in DiVA

No full text

Other links

Publisher's full text

Search in DiVA

By author/editor
Křepela, Martin
By organisation
Department of Mathematics and Computer Science
In the same journal
Mathematical Inequalities & Applications
Mathematical Analysis

Search outside of DiVA

GoogleGoogle Scholar

Altmetric score

Total: 182 hits
ReferencesLink to record
Permanent link

Direct link