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Lundberg, Staffanorcid.org/0000-0002-6058-6512

Open this publication in new window or tab >>Multi–dimensional Hardy type inequalities in Hölder spaces### Burtseva, Evgeniya

### Lundberg, Staffan

### Persson, Lars-Erik

### Samko, Natasha

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_some",{id:"formSmash:j_idt184:0:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_otherAuthors",{id:"formSmash:j_idt184:0:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 12, no 3, p. 719-729Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Zagreb: Element, 2018
##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-69692 (URN)10.7153/jmi-2018-12-55 (DOI)000445366500010 ()
#####

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##### Note

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UiT, The Arctic University of Norwa.

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.

Most Hardy type inequalities concern boundedness of the Hardy type operators in Lebesgue spaces. In this paper we prove some new multi-dimensional Hardy type inequalities in Hölder spaces.

Validerad;2018;Nivå 2;2018-06-26 (andbra)

Available from: 2018-06-19 Created: 2018-06-19 Last updated: 2018-10-15Bibliographically approvedOpen this publication in new window or tab >>Studies of some Operators of Harmonic Analysis in certain Function Spaces with Applications to PDEs### Lundberg, Staffan

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); 2018 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Narvik: UiT The Arctic University of Norway, 2018. p. 93
##### Keywords

Operators, Hardy Operators, Potential Operators, Singular Operators, Function Spaces, Morrey Spaces, H¨older Spaces, Partial Differential Equations, Inequalities, Hardy Type Inequalities, Weights, Applications
##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-71990 (URN)978-82-7823-212-5 (ISBN)978-82-7823-213-2 (ISBN)
#####

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Available from: 2018-12-13 Created: 2018-12-11 Last updated: 2019-02-18Bibliographically approved

Faculty of Science and Technology, Department of Computer Science and Computational Engineering, UiT The Arctic University of Norway, Narvik, Norway.

The study in this PhD thesis aims at development of certain mathematical methods used in applications, in particular, in the study of regularity properties of solutions in various mathematical models described by Partial Differential Equations (PDEs). To this end, we study various operators of harmonic analysis in certain function spaces, since solutions to many PDEs may be expressed in terms of such operators.

This PhD thesis consists of four papers (papers A–D) and an Introduction.

In Paper A we introduce a version of weighted anisotropic mixed norm Morrey spaces and anisotropic Hardy operators. We derive conditions for boundedness of these operators in such spaces. We also reveal the role of these operators in the solving of some degenerate hyperbolic PDEs of some class.

In Paper B we prove the boundedness of potential operators in weighted generalised Morrey space in terms of Matuszewska-Orlicz indices of weights and apply this result to the Helmholtz equationin R^{3} with a free term in such a space. We also give a short overview of some typical situations when potential type operators arise when solving PDEs.

In Paper C we study the boundedness of some multidimensional Hardy type operators in Hölder spaces and derive some new results of interest also in the theory of inequalities.

In Paper D we prove some differentiation formulas for weighted singular integrals, which we suppose to apply in our future studies concerning the solution of some integral equations of the first kind.

These new results are put into a more general frame in an Introduction, where also crucial parts of previous research by the candidate (e.g. published in two Licentiate theses) are briefly described. Note, in particular, that this PhD thesis may be regarded as a more theoretically based continuation of the Licentiate thesis in Wood Technology. This important link is carefully described in the Introduction.

Open this publication in new window or tab >>On some hyperbolic type equations and weighted anisotropic Hardy operators### Lundberg, Staffan

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.### Samko, Natasha

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_some",{id:"formSmash:j_idt184:2:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_otherAuthors",{id:"formSmash:j_idt184:2:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_otherAuthors",multiple:true}); 2017 (English)In: Mathematical methods in the applied sciences, ISSN 0170-4214, E-ISSN 1099-1476, Vol. 40, no 5, p. 1414-1421Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

John Wiley & Sons, 2017
##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-5677 (URN)10.1002/mma.4062 (DOI)000397303100005 ()2-s2.0-85014096145 (Scopus ID)3d785572-32c1-4148-9804-35574a6ad14f (Local ID)3d785572-32c1-4148-9804-35574a6ad14f (Archive number)3d785572-32c1-4148-9804-35574a6ad14f (OAI)
#####

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#####

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#####

##### Note

We introduce a version of weighted anisotropic Morrey spaces and anisotropic Hardy operators. We find conditions for boundedness of these operators in such spaces. We also reveal the role of these operators in solving some classes of degenerate hyperbolic partial differential equations.

Validerad; 2017; Nivå 2; 2017-03-07 (andbra)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-09-14Bibliographically approvedOpen this publication in new window or tab >>Potential type operators in PDEs and their applications### Burtseva, Evgeniya

### Lundberg, Staffan

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.### Persson, Lars-Erik

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.### Samko, Natasha

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); 2017 (English)In: AIP Conference Proceedings, ISSN 0094-243X, E-ISSN 1551-7616, Vol. 1798, article id 020178Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

AIP Publishing, 2017
##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-62316 (URN)10.1063/1.4972770 (DOI)000399203000177 ()2-s2.0-85013628861 (Scopus ID)
##### Conference

11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2016, La Rochelle, France, 4-8 July 2016
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_j_idt359",{id:"formSmash:j_idt184:3:j_idt188:j_idt359",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_j_idt359",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_j_idt365",{id:"formSmash:j_idt184:3:j_idt188:j_idt365",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_j_idt365",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_j_idt371",{id:"formSmash:j_idt184:3:j_idt188:j_idt371",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_j_idt371",multiple:true});
#####

##### Note

We prove the boundedness of Potential operator in weighted generalized Morrey space in terms of Matuszewska-Orlicz indices of weights and apply this result to the Hemholtz equation in r^{3} with a free term in such a space. We also give a short overview of some typical situations when Potential type operators arise when solving PDEs.

2017-03-03 (andbra);Konferensartikel i tidskrift

Available from: 2017-03-06 Created: 2017-03-06 Last updated: 2018-11-20Bibliographically approvedOpen this publication in new window or tab >>On precise differentiation formula for weighted singular integrals of Sobolev functions### Lundberg, Staffan

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); 2014 (English)In: 10th International conference on mathematical problems in engineering, aerosace and sciences: ICNPAA 2014 : Narvik, Norway, 15–18 July 2014 / [ed] Seenith Sivasundaram, Melville, NY: American Institute of Physics (AIP), 2014, p. 621-626Conference paper, Published paper (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Melville, NY: American Institute of Physics (AIP), 2014
##### Series

A I P Conference Proceedings Series, ISSN 0094-243X ; 1637
##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-39608 (URN)10.1063/1.4904632 (DOI)e7004fa9-2c01-4ce9-8480-66569ec48931 (Local ID)978-0-7354-1276-7 (ISBN)e7004fa9-2c01-4ce9-8480-66569ec48931 (Archive number)e7004fa9-2c01-4ce9-8480-66569ec48931 (OAI)
##### Conference

International conference on mathematical problems in engineering, aerosace and sciences : 15/07/2014 - 18/07/2014
#####

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##### Note

Godkänd; 2014; 20141215 (lund)Available from: 2016-10-03 Created: 2016-10-03 Last updated: 2018-03-09Bibliographically approved

In various applications there appear integral equations of the first kind with a kernel which has a logarithmic singularity. The corresponding classes of well-posedness for such equations are Sobolev spaces. We prove the differentiation formulas for weighted singular integrals, which appear in such study, with the goal of its further application to integral equations.

Open this publication in new window or tab >>Invertible Bäcklund transformations for autonomous evolution equations### Euler, Marianna

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.### Euler, Norbert

### Lundberg, Staffan

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); 2009 (Russian)In: Theoretical and mathematical physics, ISSN 0040-5779, E-ISSN 1573-9333, Vol. 159, no 3, p. 418-427Article in journal (Refereed) Published
##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-6414 (URN)4a2cd480-4d3d-11df-a0f4-000ea68e967b (Local ID)4a2cd480-4d3d-11df-a0f4-000ea68e967b (Archive number)4a2cd480-4d3d-11df-a0f4-000ea68e967b (OAI)
#####

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##### Note

Godkänd; 2009; 20100421 (andbra)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-03-09Bibliographically approved

Open this publication in new window or tab >>On adjoint symmetries and reciprocal Bäcklund transformations of evolution equations### Lundberg, Staffan

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_some",{id:"formSmash:j_idt184:6:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_otherAuthors",{id:"formSmash:j_idt184:6:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_otherAuthors",multiple:true}); 2009 (English)Licentiate thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Luleå: Luleå tekniska universitet, 2009. p. 83
##### Series

Licentiate thesis / Luleå University of Technology, ISSN 1402-1757
##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-26553 (URN)ed224690-e2d9-11dd-981b-000ea68e967b (Local ID)978-91-86233-08-2 (ISBN)ed224690-e2d9-11dd-981b-000ea68e967b (Archive number)ed224690-e2d9-11dd-981b-000ea68e967b (OAI)
#####

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##### Note

Godkänd; 2009; 20090115 (lund); Licentiatseminarium för avläggande av teknologie licentiatexamen. Examinator: Docent Marianna Euler, Luleå tekniska universitet Tid: Fredag den 20 mars 2009 kl 10.15 Plats: D2222, Luleå tekniska universitetAvailable from: 2016-09-30 Created: 2016-09-30 Last updated: 2018-03-09Bibliographically approved

The aim of this Licentiate Thesis is to discuss special transformations and so-called adjoint symmetries of nonlinear partial differential equations. Nonlinear partial differential equations play an important role in the description of many physical phenomena. In order to understand the phenomena, modelled by the equations mentioned above, it is therefore necessary to obtain and analyze the solutions and the conservation laws of these equations. In this Thesis we investigate some methods to obtain conservation laws and transformations between nonlinear partial differential equations and moreover to classify nonlinear partial differential equations with respect to those methods.The main emphasis is on adjoint symmetries and transformations of evolution equations. In particular we study the adjoint symmetries and the construction of reciprocal Bäcklund transformations for evolution equations.

Open this publication in new window or tab >>Reciprocal Bäcklund transformations of autonomous evolution equations### Euler, Marianna

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.### Euler, Norbert

### Lundberg, Staffan

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_some",{id:"formSmash:j_idt184:7:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_otherAuthors",{id:"formSmash:j_idt184:7:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_otherAuthors",multiple:true}); 2009 (English)In: Theoretical and mathematical physics, ISSN 0040-5779, E-ISSN 1573-9333, Vol. 159, no 3, p. 770-778Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-4706 (URN)10.1007/s11232-009-0065-8 (DOI)2-s2.0-70350026533 (Scopus ID)2b038480-88e6-11de-8da0-000ea68e967b (Local ID)2b038480-88e6-11de-8da0-000ea68e967b (Archive number)2b038480-88e6-11de-8da0-000ea68e967b (OAI)
#####

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##### Note

Validerad; 2009; 20090814 (norbert)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

We discuss the construction of reciprocal Bäcklund transformations for evolution equations using integrating factors of zeroth and higher orders with their corresponding conservation laws. As an example, we consider the Harry Dym equation and the Schwarzian KdV equation.

Open this publication in new window or tab >>On adjoint symmetries of a class of evolution equations### Lundberg, Staffan

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_some",{id:"formSmash:j_idt184:8:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_otherAuthors",{id:"formSmash:j_idt184:8:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_otherAuthors",multiple:true}); 2008 (English)Report (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Luleå: Department of Mathematics, Luleå University of Technology, 2008. p. 18
##### Series

Gula serien, ISSN 1400-4003 ; 2008:08
##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-23172 (URN)5e0d7b80-e2db-11dd-981b-000ea68e967b (Local ID)5e0d7b80-e2db-11dd-981b-000ea68e967b (Archive number)5e0d7b80-e2db-11dd-981b-000ea68e967b (OAI)
#####

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##### Note

Godkänd; 2008; 20090115 (lund)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-03-09Bibliographically approved

In this Paper we study the adjoint symmetries for a class of third-order evolution equations in (1+1) dimensions. We assume that the equations admit adjoint symmetries of maximum order 2, and we obtain the complete classification with respect to this property. Examples of adjoint symmetries and integrating factors for the Korteweg-de Vries and the Schwarzian-Korteweg-de Vries equations are given.

Open this publication in new window or tab >>Erratum: Studies of non-contact methods for roughness measurements on wood surfaces### Lundberg, Staffan

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.### Porankiewicz, B.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_some",{id:"formSmash:j_idt184:9:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_otherAuthors",{id:"formSmash:j_idt184:9:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_otherAuthors",multiple:true}); 1996 (English)In: European Journal of Wood and Wood Products, ISSN 0018-3768, E-ISSN 1436-736X, Vol. 54, p. 72-Article in journal (Refereed) Published
##### National Category

Other Mechanical Engineering Mathematical Analysis
##### Research subject

Wood Technology; Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-6536 (URN)4c2ea010-0867-11dc-b09b-000ea68e967b (Local ID)4c2ea010-0867-11dc-b09b-000ea68e967b (Archive number)4c2ea010-0867-11dc-b09b-000ea68e967b (OAI)
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##### Note

Godkänd; 1996; 20070522 (cira)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-03-09Bibliographically approved

Agriculture University of Pouznan.