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Continuous functions and Riesz type potentials in homogeneous spaces
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2015 (English)In: Potential Analysis, ISSN 0926-2601, E-ISSN 1572-929X, Vol. 43, no 3, 495-511 p.Article in journal (Refereed) Published
Abstract [en]

We develop a potential theory for a Riesz type kernel in a homogeneous space and characterize the compact sets K with capacity zero as the sets K for which every continous function f on K is the restriction to K of a continuous potential Uσfk of an absolutely continuous measure σ f supported in an arbitrarily small neighbourhood of K. The measure σ f can be choosen as a suitable restriction of a single measure σ that only depends on the set K and the kernel k.

Place, publisher, year, edition, pages
New York: Springer-Verlag New York, 2015. Vol. 43, no 3, 495-511 p.
Keyword [en]
Homogeneous space, doubling measure, kernel, potential, energy, capacity, dyadic cubes
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-104307DOI: 10.1007/s11118-015-9483-4ISI: 000365769100008OAI: oai:DiVA.org:umu-104307DiVA: diva2:818931
Available from: 2015-06-09 Created: 2015-06-09 Last updated: 2017-12-04Bibliographically approved

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Sjödin, Tord

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