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Hardy and singular operators in weighted generalized Morrey spaces with applications to singular integral equations
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Narvik University College, 8505 Narvik, Norway.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.ORCID iD: 0000-0002-8595-4326
2012 (English)In: Mathematical methods in the applied sciences, ISSN 0170-4214, E-ISSN 1099-1476, Vol. 35, no 11, p. 1300-1311Article in journal (Refereed) Published
Abstract [en]

We study the weighted boundedness of the multi-dimensional Hardy-type and singular operators in the generalized Morrey spaces L p,Ψ(ℝ n,w), defined by an almost increasing function Ψ(r) and radial type weights. We obtain sufficient conditions, in terms of numerical characteristics, that is, index numbers of the weight functions and the function Ψ. In relation with the wide usage of singular integral equations in applications, we show how the solvability of such equations in the generalized Morrey spaces depends on the main characteristics of the space, which allows to better control both the singularities and regularity of solutions

Place, publisher, year, edition, pages
2012. Vol. 35, no 11, p. 1300-1311
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-4343DOI: 10.1002/mma.2532ISI: 000305741100005Scopus ID: 2-s2.0-84863185607Local ID: 2473245e-cdd1-4300-9059-07ed929231bdOAI: oai:DiVA.org:ltu-4343DiVA, id: diva2:977208
Note
Validerad; 2012; 20120806 (ysko)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2023-09-05Bibliographically approved

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Lukkassen, DagPersson, Lars-ErikSamko, Natasha

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