Properties of capacities generated by Sobolev classes on metric measure spaces

S. A. Bondarev

Trudy Instituta matematiki, Tome 24 (2016) no. 2, pp. 20-31.

Résumé

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.

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