Compactness of Embeddings of Sobolev Type on Metric Measure Spaces

I. A. Ivanishko ; V. G. Krotov

Matematičeskie zametki, Tome 86 (2009) no. 6, pp. 829-844.

Résumé

We establish conditions for the compactness of embeddings for some classes of functions on metric space with measure satisfying the duplication condition. These classes are defined in terms of the $L^p$-summability of maximal functions measuring local smoothness.

Détail

Keywords: embedding of Sobolev type, metric measure space, Hardy–Littlewood maximal function, Hölder class, Sobolev space, Borel measure
Mots-clés : Lebesgue measure.

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