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Samko, Natashaorcid.org/0000-0002-8595-4326

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 >>Commutators with Coefficients in CMO of Weighted Hardy Operators in Generalized Local Morrey Spaces### Samko, Natasha

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.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}); 2017 (English)In: Mediterranean Journal of Mathematics, ISSN 1660-5446, E-ISSN 1660-5454, Vol. 14, no 2, article id 64Article in journal (Refereed) Published
##### Abstract [en]

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

Springer, 2017
##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-62481 (URN)10.1007/s00009-017-0872-3 (DOI)000396095300030 ()2-s2.0-85014458324 (Scopus ID)
#####

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##### Note

We prove theorems on the boundedness of commutators [a,Hwα] of the weighted multidimensional Hardy operator Hwα:=wHα1w from a generalized local Morrey space L^{p} ^{,} ^{φ} ^{;} ^{0}(R^{n}) to local or global space L^{q} ^{,} ^{ψ}(R^{n}). The main impacts of these theorems are1.the use of CMO_{s}-class of coefficients a for the commutators;2.the general setting when the function φ defining the Morrey space and the weight w are independent of one another and the weight w is not assumed to be in A_{p};3.recovering the Sobolev–Adams exponent q instead of Sobolev–Spanne type exponent in the case of classical Morrey spaces4.boundedness from local to global Morrey spaces;5.the obtained estimates contain the parameter s> 1 which may be arbitrarily chosen. Its choice regulates in fact an equilibrium between assumptions on the coefficient a and the characteristics of the space. The obtained results are new also in non-weighted case

Validerad; 2017; Nivå 2; 2017-03-14 (andbra)

Available from: 2017-03-14 Created: 2017-03-14 Last updated: 2018-09-14Bibliographically approvedOpen this publication in new window or tab >>Hardy type inequalities with kernels: The current status and some new results### Kufner, Alois

### 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_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: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 290, no 1, p. 57-65Article 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-13062 (URN)10.1002/mana.201500363 (DOI)000395223100006 ()2-s2.0-84992089804 (Scopus ID)c37ca8b9-9e8d-4ac5-a216-6bbf39523689 (Local ID)c37ca8b9-9e8d-4ac5-a216-6bbf39523689 (Archive number)c37ca8b9-9e8d-4ac5-a216-6bbf39523689 (OAI)
#####

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##### Note

Mathematical Institute, Czech Academy of Sciences, Department of Mathematics, University of West Bohemia.

We consider the general Hardy type operator inline image where inline image is a positive and measurable kernel. To characterize the weights u and v so that inline image is still an open problem for any parameters p and q. However, for special cases the solution is known for some parameters p and q. In this paper the current status of this problem is described and discussed mainly for the case inline image In particular, some new scales of characterizations in classical situations are described, some new proofs and results are given and open questions are raised.

Validerad; 2017; Nivå 2; 2017-02-21 (rokbeg)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-09-14Bibliographically approvedOpen 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_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: 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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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});
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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 >>On weighted generalized fractional and Hardy-type operators acting between Morrey-type spaces### Burtseva, Evgeniya

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_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}); 2017 (English)In: Fractional Calculus and Applied Analysis, ISSN 1311-0454, E-ISSN 1314-2224, Vol. 20, no 6, p. 1545-1566Article in journal (Refereed) Published
##### Abstract [en]

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

Walter de Gruyter, 2017
##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-67715 (URN)10.1515/fca-2017-0081 (DOI)000424675400013 ()2-s2.0-85041948540 (Scopus ID)
#####

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##### Note

We study weighted generalized Hardy and fractional operators acting from generalized Morrey spaces L^{p,φ},(^{n}) into Orlicz-Morrey spaces L^{Φ,φ},(^{n}). We deal with radial quasi-monotone weights and assumptions imposed on weights are given in terms of Zigmund-type integral conditions. We find conditions on φ,Φ, the weight w and the kernel of the fractional operator, which insures such a boundedness. We prove some pointwise estimates for weighted generalized fractional operators via generalized Hardy operators, which allow to obtain the weighted boundedness for fractional operators from those for Hardy operators. We provide also some easy to check numerical inequalities to verify the obtained conditions.

Validerad;2018;Nivå 2;2018-02-21 (andbra)

Available from: 2018-02-21 Created: 2018-02-21 Last updated: 2019-04-23Bibliographically 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_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}); 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
#####

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##### 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 >>Weighted inequalities of Hardy type### Kufner, Alois

### 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_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}); 2017 (English)Book (Other academic)
##### Abstract [en]

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

Singapore: World Scientific and Engineering Academy and Society, 2017. p. 480 Edition: 2
##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-65569 (URN)978-981-3140-64-6 (ISBN)
#####

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Available from: 2017-09-11 Created: 2017-09-11 Last updated: 2018-03-07Bibliographically approved

Mathematical Institute, Czech Academy of Sciences.

In this second edition, all chapters in the first edition have been updated with new information. Moreover, a new chapter contains new and complementary information concerning: (a) a convexity approach to prove and explain Hardy-type inequalities; (b) sharp constants; (c) scales of inequalities to characterize Hardy-type inequalities; (d) Hardy-type inequalities in other function spaces; and (e) a number of new open questions.

Open this publication in new window or tab >>Calderón–Zygmund Type Singular Operators in Weighted Generalized Morrey Spaces### 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.### Wall, Peter

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.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}); 2016 (English)In: Journal of Fourier Analysis and Applications, ISSN 1069-5869, E-ISSN 1531-5851, Vol. 22, no 2, p. 413-426Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-10724 (URN)10.1007/s00041-015-9418-x (DOI)000376247200006 ()2-s2.0-84932141263 (Scopus ID)9917e8f0-0d9f-4e92-a533-ccebb01d4459 (Local ID)9917e8f0-0d9f-4e92-a533-ccebb01d4459 (Archive number)9917e8f0-0d9f-4e92-a533-ccebb01d4459 (OAI)
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##### Note

Validerad; 2016; Nivå 2; 20150624 (andbra)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

We find conditions for the weighted boundedness of a general class of multidimensional singular integral operators in generalized Morrey spaces L p,φ (R n ,w), defined by a function φ(x,r) and radial type weight w(|x−x 0 |),x 0 ∈R n . These conditions are given in terms of inclusion into L p,φ (R n ,w), of a certain integral constructions defined by φ and w. In the case of φ=φ(r) we also provide easy to check sufficient conditions for that in terms of indices of φ and w.

Open this publication in new window or tab >>Weighted Adams type theorem for the Riesz fractional integral in generalized Morrey Space### Burtseva, Evgeniya

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_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}); 2016 (English)In: Fractional Calculus and Applied Analysis, ISSN 1311-0454, E-ISSN 1314-2224, Vol. 19, no 4, p. 954-972Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-59748 (URN)10.1515/fca-2016-0052 (DOI)000383390700014 ()2-s2.0-84985023407 (Scopus ID)
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##### Note

We prove the boundedness of the Riesz fractional integration operator from a generalized Morrey space L-p,L-phi to a certain Orlicz-Morrey space L-Phi,L-phi which covers the Adams result for Morrey spaces. We also give a generalization to the case of weighted Riesz fractional integration operators for some class of weights.

Validerad; 2016; Nivå 2; 2016-10-14 (andbra)

Available from: 2016-10-14 Created: 2016-10-14 Last updated: 2018-10-04Bibliographically approvedOpen this publication in new window or tab >>Hardy Type Operators in Local Vanishing Morrey Spaces on Fractal Sets### Lukkassen, Dag

### 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_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}); 2015 (English)In: Fractional Calculus and Applied Analysis, ISSN 1311-0454, E-ISSN 1314-2224, Vol. 18, no 5, p. 1252-1276Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-2477 (URN)10.1515/fca-2015-0072 (DOI)000366044900009 ()2-s2.0-84946565894 (Scopus ID)0189b172-870a-49fa-80ea-8d186fd3b653 (Local ID)0189b172-870a-49fa-80ea-8d186fd3b653 (Archive number)0189b172-870a-49fa-80ea-8d186fd3b653 (OAI)
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##### Note

Validerad; 2015; Nivå 2; 20151020 (andbra)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

Narvik University College and Norut Narvik.

We obtain two-weighted estimates for the Hardy type operators fromlocal generalized Morrey spaces Lp,ϕloc (X,w1) defined on an arbitrary underlyingquasi-metric measure space (X, μ, ) with the growth condition, toLq,ψloc (X,w2), where w1 = w1[(x, x0)], x0 ∈ X is a weight of radial type,while w2 = w2(x) may be an arbitrary weight. The proof allows to simultaneouslytreat a similar boundedness V Lp,ϕloc (X,w1) → V Lq,ψloc (X,w2) forvanishing Morrey spaces. We obtain sufficient conditions for such estimatesin terms of some integral inequalities imposed on ϕ, ψ and w1.w2. We alsospecially treat the one weight case where w2(x) is also of radial type. Wedo not impose doubling condition on the measure μ, but base our result onthe growth condition.The obtained results show the explicit dependence of the mapping propertiesof the Hardy type operators on the fractional dimension of the set(X, μ, ). An application to spherical Hardy type operators is also given.