Geodesic
Compactness of Embeddings of Sobolev Type on Metric Measure Spaces
Matematičeskie zametki, Tome 86 (2009) no. 6, pp. 829-844

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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.
Keywords: embedding of Sobolev type, metric measure space, Hardy–Littlewood maximal function, Hölder class, Sobolev space, Borel measure
Mots-clés : Lebesgue measure. 
@article{MZM_2009_86_6_a2,
     author = {I. A. Ivanishko and V. G. Krotov},
     title = {Compactness of {Embeddings} of {Sobolev} {Type} on {Metric} {Measure} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {829--844},
     publisher = {mathdoc},
     volume = {86},
     number = {6},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_86_6_a2/}
}
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I. A. Ivanishko; V. G. Krotov. Compactness of Embeddings of Sobolev Type on Metric Measure Spaces. Matematičeskie zametki, Tome 86 (2009) no. 6, pp. 829-844. http://geodesic.mathdoc.fr/item/MZM_2009_86_6_a2/