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Wall, Peterorcid.org/0000-0001-8211-3671

Open this publication in new window or tab >>New insights on lubrication theory for compressible fluids### Almqvist, Andreas

### Burtseva, Evgeniya

### Ràfols, Francesc Pérez

### Wall, Peter

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}); 2019 (English)In: International Journal of Engineering Science, ISSN 0020-7225, E-ISSN 1879-2197, Vol. 145, article id 103170Article in journal (Refereed) Published
##### Abstract [en]

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

Elsevier, 2019
##### Keywords

Thin film approximation, Reynold’s equation, Compressible flow, Navier–Stokes equations, Dimension reduction, Asymptotic analysis
##### National Category

Mathematical Analysis Tribology (Interacting Surfaces including Friction, Lubrication and Wear)
##### Research subject

Machine Elements; Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-76138 (URN)10.1016/j.ijengsci.2019.103170 (DOI)2-s2.0-85072601607 (Scopus ID)
#####

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##### Note

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.

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

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.

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

The fact that the film is thin is in lubrication theory utilised to simplify the full Navier–Stokes system of equations. For incompressible and iso-viscous fluids, it turns out that the inertial terms are small enough to be neglected. However, for a compressible fluid, we show that the influence of inertia depends on the (constitutive) density-pressure relationship and may not always be neglected. We consider a class of iso-viscous fluids obeying a power-law type of compressibility, which in particular includes both incompressible fluids and ideal gases. We show by scaling and asymptotic analysis, that the degree of compressibility determines whether the terms governing inertia may or may not be neglected. For instance, for an ideal gas, the inertial terms remain regardless of the film height-to-length ratio. However, by means of a specific modified Reynolds number that we define we show that the magnitudes of the inertial terms rarely are large enough to be influential. In addition, we consider fluids obeying the well-known Dowson and Higginson density-pressure relationship and show that the inertial terms can be neglected, which allows for obtaining a Reynolds type of equation. Finally, some numerical examples are presented in order to illustrate our theoretical results.

Validerad;2019;Nivå 2;2019-09-27 (johcin)

Available from: 2019-09-27 Created: 2019-09-27 Last updated: 2019-10-02Bibliographically approvedOpen this publication in new window or tab >>Pressure-driven flow in thin domains### Fabricius, John

### Miroshnikova, Elena

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

### Wall, Peter

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}); 2019 (English)In: Asymptotic Analysis, ISSN 0921-7134, E-ISSN 1875-8576Article in journal (Refereed) Epub ahead of print
##### Abstract [en]

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

IOS Press, 2019
##### Keywords

Stokes equation, pressure boundary condition, two-scale convergence, thin domain, Bogovskii operator, Korn inequality
##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-75853 (URN)10.3233/ASY-191535 (DOI)
#####

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Available from: 2019-09-05 Created: 2019-09-05 Last updated: 2019-09-05

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

Department of Mathematics and Informatics, Eduardo Mondlane University, Maputo, Mozambique.

We study the asymptotic behavior of pressure-driven Stokes flow in a thin domain. By letting the thickness of the domain tend to zero we derive a generalized form of the classical Reynolds–Poiseuille law, i.e. the limit velocity field is a linear function of the pressure gradient. By prescribing the external pressure as a normal stress condition, we recover a Dirichlet condition for the limit pressure. In contrast, a Dirichlet condition for the velocity yields a Neumann condition for the limit pressure.

Open this publication in new window or tab >>On an approximation of 2-dimensional Walsh–Fourier series in martingale Hardy spaces### Persson, Lars-Erik

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

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_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}); 2018 (English)In: Annals of Functional Analysis, ISSN 2008-8752, E-ISSN 2008-8752, Vol. 9, no 1, p. 137-150Article in journal (Refereed) Published
##### Abstract [en]

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

Duke University Press, 2018
##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-63509 (URN)10.1215/20088752-2017-0032 (DOI)000432617900012 ()2-s2.0-85041646355 (Scopus ID)
#####

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##### Note

In this paper, we investigate convergence and divergence of partial sums with respect to the 2-dimensional Walsh system on the martingale Hardy spaces. In particular, we find some conditions for the modulus of continuity which provide convergence of partial sums of Walsh-Fourier series. We also show that these conditions are in a sense necessary and suffcient.

Validerad;2018;Nivå 2;2018-02-19 (svasva)

Available from: 2017-05-23 Created: 2017-05-23 Last updated: 2018-06-08Bibliographically approvedOpen this publication in new window or tab >>On the Nörlund logarithmic means with respect to Vilenkin system in the Martingale Hardy Space _{H1}### Persson, Lars-Erik

### Tephnadze, George

### Wall, Peter

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}); 2018 (English)In: Acta Mathematica Hungarica, ISSN 0236-5294, E-ISSN 1588-2632, Vol. 154, no 2, p. 289-301Article in journal (Refereed) Published
##### Abstract [en]

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

Springer, 2018
##### Keywords

Vilenkin system, Nörlund logarithmic mean, partial sum, modulus of continuity, Hardy space
##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-66424 (URN)10.1007/s10474-017-0773-8 (DOI)000427375600003 ()
#####

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##### Note

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. RUDN University, Moscow, Russia; UiT The Arctic University of Norway.

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. School of Informatics, Engineering and Mathematics, The University of Georgia.

We prove and discuss a new divergence result of Nörlund logarithmic means with respect to Vilenkin system in Hardy space H1.

Validerad;2018;Nivå 2;2018-03-14 (rokbeg)

Available from: 2017-11-07 Created: 2017-11-07 Last updated: 2018-04-03Bibliographically approvedOpen this publication in new window or tab >>A Comparison of the Roughness Regimes in Hydrodynamic Lubrication### Fabricius, John

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.### Tsandzana, Afonso Fernando

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.### Pérez-Ràfols, Francesc

### Wall, Peter

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: Journal of tribology, ISSN 0742-4787, E-ISSN 1528-8897, Vol. 139, no 5, article id 051702Article in journal (Refereed) Published
##### Abstract [en]

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

The American Society of Mechanical Engineers (ASME), 2017
##### National Category

Mathematical Analysis Tribology (Interacting Surfaces including Friction, Lubrication and Wear)
##### Research subject

Mathematics; Machine Elements
##### Identifiers

urn:nbn:se:ltu:diva-64734 (URN)10.1115/1.4035868 (DOI)000406397500016 ()2-s2.0-85020933899 (Scopus ID)
#####

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##### Note

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.

This work relates to previous studies concerning the asymptotic behavior of Stokes flow in a narrow gap between two surfaces in relative motion. It is assumed that one of the surfaces is rough, with small roughness wavelength l, so that the film thickness h becomes rapidly oscillating. Depending on the limit of the ratio h/l, denoted as k, three different lubrication regimes exist: Reynolds roughness (k-0), Stokes roughness (0<γ<1), and high-frequency roughness (γ = ∞). In each regime, the pressure field is governed by a generalized Reynolds equation, whose coefficients (so-called flow factors) depend on k. To investigate the accuracy and applicability of the limit regimes, we compute the Stokes flow factors for various roughness patterns by varying the parameter k. The results show that there are realistic surface textures for which the Reynolds roughness is not accurate and the Stokes roughness must be used instead.

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

Available from: 2017-07-03 Created: 2017-07-03 Last updated: 2018-11-27Bibliographically approvedOpen this publication in new window or tab >>Additive weighted Lp estimates of some classes of integral operators involving generalized Oinarov Kernels### Abylayeva, A.M.

### Baiarystanov, A.O.

### Persson, Lars-Erik

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_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: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 11, no 3, p. 683-694Article in journal (Refereed) Published
##### Abstract [en]

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

Ele-Math, 2017
##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-60850 (URN)10.7153/jmi-2017-11-54 (DOI)000411883200006 ()2-s2.0-85029774121 (Scopus ID)
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##### Note

L. N.Gumilev Eurasian National University, Khazakstan.

L. N.Gumilev Eurasian National University, Khazakstan.

Abstract. Inequalities of the formkuK f kq 6C(kr f kp +kvH f kp) , f > 0,are considered, where K is an integral operator of Volterra type and H is the Hardy operator.Under some assumptions on the kernel K we give necessary and sufficient conditions for suchan inequality to hold.1

Validerad;2017;Nivå 2;2017-09-08 (andbra)

Available from: 2016-12-01 Created: 2016-12-01 Last updated: 2017-11-24Bibliographically approvedOpen this publication in new window or tab >>Flow in thin domains with a microstructure: Lubrication and thin porous media### Almqvist, Andreas

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.### Fabricius, John

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

### Wall, Peter

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)In: AIP Conference Proceedings, ISSN 0094-243X, E-ISSN 1551-7616, Vol. 1798, article id 020172Article in journal (Refereed) Published
##### Abstract [en]

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

AIP Publishing, 2017
##### National Category

Mathematical Analysis Tribology (Interacting Surfaces including Friction, Lubrication and Wear) Fluid Mechanics and Acoustics
##### Research subject

Machine Elements; Mathematics; Fluid Mechanics
##### Identifiers

urn:nbn:se:ltu:diva-62224 (URN)10.1063/1.4972764 (DOI)000399203000171 ()2-s2.0-85013665597 (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

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.

This paper is devoted to homogenization of different models of flow in thin domains with a microstructure. The focus is on applications connected to the effect of surface roughness in full film lubrication, but a parallel to flow in thin porous media is also discussed. Mathematical models of such flows naturally include two small parameters. One is connected to the fluid film thickness and the other to the microstructure. The corresponding asymptotic analysis is a delicate problem, since the result depends on how fast the two small parameters tend to zero relative to each other. We give a review of the current status in this area and point out some future challenges.

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

Available from: 2017-03-01 Created: 2017-03-01 Last updated: 2018-11-20Bibliographically approvedOpen this publication in new window or tab >>Homogenization of the Stokes equation with mixed boundary condition in a porous medium### Fabricius, John

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

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}); 2017 (English)In: Cogent Mathamatics, E-ISSN 2331-1835, Vol. 4, no 1, article id 1327502Article in journal (Refereed) Published
##### Abstract [en]

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

Taylor & Francis, 2017
##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-64001 (URN)10.1080/23311835.2017.1327502 (DOI)000403291100001 ()
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##### Note

We homogenize stationary incompressible Stokes flow in a periodic porous medium. The fluid is assumed to satisfy a no-slip condition on the boundary of solid inclusions and a normal stress (traction) condition on the global boundary. Under these assumptions, the homogenized equation becomes the classical Darcy law with a Dirichlet condition for the pressure.

Validerad;2017;Nivå 2;2017-07-06 (rokbeg)

Available from: 2017-06-14 Created: 2017-06-14 Last updated: 2018-07-10Bibliographically approvedOpen this publication in new window or tab >>A stochastic two-scale model for pressure-driven flow between rough surfaces### Rafols, Francesc Perez

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.### Larsson, Roland

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.### Lundström, Staffan

### Wall, Peter

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}); ### Almqvist, Andreas

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.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}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt184_8_j_idt188_j_idt202",{id:"formSmash:j_idt184:8:j_idt188:j_idt202",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_j_idt202",onLabel:"Hide others...",offLabel:"Show others..."}); 2016 (English)In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 472, no 2190, article id 20160069Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Tribology (Interacting Surfaces including Friction, Lubrication and Wear) Fluid Mechanics and Acoustics Mathematical Analysis
##### Research subject

Machine Elements; Fluid Mechanics; Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-14714 (URN)10.1098/rspa.2016.0069 (DOI)000379726800016 ()2-s2.0-84978388150 (Scopus ID)e22df646-269f-4f4e-80d7-43e89b5a630a (Local ID)e22df646-269f-4f4e-80d7-43e89b5a630a (Archive number)e22df646-269f-4f4e-80d7-43e89b5a630a (OAI)
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##### Note

Validerad; 2016; Nivå 2; 20160816 (andbra)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.

Seal surface topography typically consists of global-scale geometric features as well as local-scale roughness details and homogenization-based approaches are, therefore, readily applied. These provide for resolving the global scale (large domain) with a relatively coarse mesh, while resolving the local scale (small domain) in high detail. As the total flow decreases, however, the flow pattern becomes tortuous and this requires a larger local-scale domain to obtain a converged solution. Therefore, a classical homogenization-based approach might not be feasible for simulation of very small flows. In order to study small flows, a model allowing feasibly-sized local domains, for really small flow rates, is developed. Realization was made possible by coupling the two scales with a stochastic element. Results from numerical experiments, show that the present model is in better agreement with the direct deterministic one than the conventional homogenization type of model, both quantitatively in terms of flow rate and qualitatively in reflecting the flow pattern.

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_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}); 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.