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Forever Young: Convolution Inequalities in Weighted Lorentz-type Spaces
Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap.ORCID-id: 0000-0003-0234-1645
2014 (engelsk)Licentiatavhandling, med artikler (Annet vitenskapelig)
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.

sted, utgiver, år, opplag, sider
Karlstad: Karlstads universitet, 2014. , s. 23
Serie
Karlstad University Studies, ISSN 1403-8099 ; 2014:21
Emneord [en]
Convolution, Young inequality, Lorentz spaces, weights, rearrangement-invariant spaces
HSV kategori
Forskningsprogram
Matematik
Identifikatorer
URN: urn:nbn:se:kau:diva-31754ISBN: 978-91-7063-552-6 (tryckt)OAI: oai:DiVA.org:kau-31754DiVA, id: diva2:706959
Presentation
2014-05-09, 3B426, Karlstads universitet, Universitetsgatan 2, Karlstad, 10:15 (engelsk)
Opponent
Veileder
Merknad

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

Tilgjengelig fra: 2014-04-17 Laget: 2014-03-24 Sist oppdatert: 2019-07-12bibliografisk kontrollert
Delarbeid
1. Convolution inequalities in weighted Lorentz spaces
Åpne denne publikasjonen i ny fane eller vindu >>Convolution inequalities in weighted Lorentz spaces
2014 (engelsk)Inngår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 17, nr 4, s. 1201-1223Artikkel i tidsskrift (Fagfellevurdert) 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.

sted, utgiver, år, opplag, sider
Croatia: Element, 2014
Emneord
Convolution, Young inequality, O’Neil inequality, Lorentz spaces, weights
HSV kategori
Forskningsprogram
Matematik
Identifikatorer
urn:nbn:se:kau:diva-31751 (URN)10.7153/mia-17-90 (DOI)000345462600001 ()
Tilgjengelig fra: 2014-03-23 Laget: 2014-03-23 Sist oppdatert: 2017-12-06bibliografisk kontrollert
2. Convolution in Rearrangement-Invariant Spaces Defined in Terms of Oscillation and the Maximal Function
Åpne denne publikasjonen i ny fane eller vindu >>Convolution in Rearrangement-Invariant Spaces Defined in Terms of Oscillation and the Maximal Function
2014 (engelsk)Inngår i: Zeitschrift für Analysis und ihre Anwendungen, ISSN 0232-2064, E-ISSN 1661-4534, Vol. 33, nr 4, s. 369-383Artikkel i tidsskrift (Fagfellevurdert) 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.

Emneord
Convolution, Young inequality, weighted Lorentz spaces, oscillation
HSV kategori
Forskningsprogram
Fysik
Identifikatorer
urn:nbn:se:kau:diva-41570 (URN)10.4171/ZAA/1517 (DOI)000347639000001 ()
Tilgjengelig fra: 2016-04-22 Laget: 2016-04-11 Sist oppdatert: 2017-11-30bibliografisk kontrollert
3. Convolution in weighted Lorentz spaces of type Γ
Åpne denne publikasjonen i ny fane eller vindu >>Convolution in weighted Lorentz spaces of type Γ
2016 (engelsk)Inngår i: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 119, nr 1, s. 113-132Artikkel i tidsskrift (Fagfellevurdert) Published
sted, utgiver, år, opplag, sider
Aarhus Universitetsforlag, 2016
Emneord
Convolution, Young inequality, Lorentz spaces, weights
HSV kategori
Forskningsprogram
Fysik
Identifikatorer
urn:nbn:se:kau:diva-31752 (URN)10.7146/math.scand.a-24187 (DOI)000383815600007 ()
Merknad

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

Tilgjengelig fra: 2014-03-23 Laget: 2014-03-23 Sist oppdatert: 2017-12-06bibliografisk kontrollert

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