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Compactness of embeddings of sobolev type on metric measure spaces

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Abstract

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.

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Authors and Affiliations

  1. Belorussian State University, Minsk, Belarus

    I. A. Ivanishko & V. G. Krotov

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  1. I. A. Ivanishko
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  2. V. G. Krotov
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Correspondence to I. A. Ivanishko.

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Original Russian Text © I. A. Ivanishko, V. G. Krotov, 2009, published in Matematicheskie Zametki, 2009, Vol. 86, No. 6, pp. 829–844.

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Ivanishko, I.A., Krotov, V.G. Compactness of embeddings of sobolev type on metric measure spaces. Math Notes 86, 775–788 (2009). https://doi.org/10.1134/S0001434609110200

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