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Trudy Instituta Matematiki, 2016, Volume 24, Number 2, Pages 20–31 (Mi timb309)  
Properties of capacities generated by Sobolev classes on metric measure spaces

S. A. Bondarev

Belarusian State University, Minsk
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Abstract: Properties of $\mathrm{Cap}_{\alpha, p}$–capacities, generated by Sobolev classes on metric spaces with doubling measure, are investigated. The principal case is $p>0$ not investigated before. It's proved that capacity is an outer measure; the property of continuity, the relation between different capacities, measure and Hausdorff dimension is investigated.
Document Type: Article
UDC: 517.5
Language: Russian
Citation: S. A. Bondarev, “Properties of capacities generated by Sobolev classes on metric measure spaces”, Tr. Inst. Mat., 24:2 (2016), 20–31
Citation in format AMSBIB
\Bibitem{Bon16}
\by S.~A.~Bondarev
\paper Properties of capacities generated by Sobolev classes on metric measure spaces
\jour Tr. Inst. Mat.
\yr 2016
\vol 24
\issue 2
\pages 20--31
\mathnet{http://mi.mathnet.ru/timb309}
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