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Hardy Type Operators in Local Vanishing Morrey Spaces on Fractal Sets
Narvik University College and Norut Narvik.
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
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]

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.

Place, publisher, year, edition, pages
2015. Vol. 18, no 5, p. 1252-1276
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-2477DOI: 10.1515/fca-2015-0072ISI: 000366044900009Scopus ID: 2-s2.0-84946565894Local ID: 0189b172-870a-49fa-80ea-8d186fd3b653OAI: oai:DiVA.org:ltu-2477DiVA, id: diva2:975329
Note
Validerad; 2015; Nivå 2; 20151020 (andbra)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

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Persson, Lars-ErikSamko, Natasha

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