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Weighted Hardy-type inequalities in variable exponent Morrey-type spaces
Narvik University College and Norut Narvik.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Universidade do Algarve, FCT, Campus de Gambelas.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.ORCID iD: 0000-0001-8211-3671
2013 (English)In: Journal of Function Spaces and Applications, ISSN 0972-6802, E-ISSN 1758-4965, article id 716029Article in journal (Refereed) Published
Abstract [en]

We study the p(.) -> q(.) boundedness of weighted multidimensional Hardy-type operators H-w(alpha(.)) and H-w(alpha(.)) of variable order alpha(x), with radial weight w(vertical bar x vertical bar), from a variable exponent locally generalized Morrey space L-p(.),L-phi(.)(R-n, w) to another L-q(.),L-psi(.)(R-n, w). The exponents are assumed to satisfy the decay condition at the origin and infinity. We construct certain functions, defined by p, alpha, and phi, the belongness of which to the resulting space L-q(.),L-psi(.)(R-n, w) is sufficient for such a boundedness. Under additional assumptions on phi/w, this condition is also necessary. We also give the boundedness conditions in terms of Zygmund-type integral inequalities for the functions phi and phi/w.

Place, publisher, year, edition, pages
2013. article id 716029
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-10057DOI: 10.1155/2013/716029ISI: 000326782100001Scopus ID: 2-s2.0-84889058552Local ID: 8cfe222e-f518-4858-be35-749ae75f18f0OAI: oai:DiVA.org:ltu-10057DiVA, id: diva2:982997
Note
Validerad; 2013; 20131205 (andbra)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

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Lukkassen, DagPersson, Lars-ErikWall, Peter

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