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Polar sets and capacitary potentials in homogeneous spaces
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2013 (English)In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 38, no 1, 771-783 p.Article in journal (Refereed) Published
Abstract [en]

A set E in a space X is called a polar set in X, relative to a kernel k(x; y), if thereis a nonnegative measure in X such that the potential Uk(x) = ∞ precisely when x ∈ E. Polarsets have been characterized in various classical cases as G-sets (countable intersections of opensets) with capacity zero. We characterize polar sets in a homogeneous space (X; d; ) for severalclasses of kernels k(x; y), among them the Riesz -kernels and logarithmic Riesz kernels. The latercase seems to be new even in Rn.

Place, publisher, year, edition, pages
Helsingfors, 2013. Vol. 38, no 1, 771-783 p.
Keyword [en]
Metric space, doubling measure, definite kernel, consistent kernel, potential, energy, capacity, polar set
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-79308DOI: 10.5186/aasfm.2013.3851OAI: oai:DiVA.org:umu-79308DiVA: diva2:640495
Available from: 2013-08-13 Created: 2013-08-13 Last updated: 2017-12-06Bibliographically approved

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