Journal
SIBERIAN MATHEMATICAL JOURNAL
Volume 54, Issue 2, Pages 353-367Publisher
MAIK NAUKA/INTERPERIODICA/SPRINGER
DOI: 10.1134/S0037446613020171
Keywords
Sobolev class; Nikol'skii class; function on a metric space; embedding theorems; compactness of embedding
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Funding
- Interdisciplinary Project of the Siberian and Far East Divisions of the Russian Academy of Sciences [56]
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We formulate a new definition of Sobolev function spaces on a domain of a metric space in which the doubling condition need not hold. The definition is equivalent to the classical definition in the case that the domain lies in a Euclidean space with the standard Lebesgue measure. The boundedness and compactness are examined of the embeddings of these Sobolev classes into L (q) and C (alpha) . We state and prove a compactness criterion for the family of functions L (p) (U), where U is a subset of a metric space possibly not satisfying the doubling condition.
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