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Sibirskii Matematicheskii Zhurnal, 2004, Volume 45, Number 2, Pages 452–465
(Mi smj1081)
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This article is cited in 5 scientific papers (total in 5 papers)
Embedding theorems for a certain function class of Sobolev type on metric spaces
A. S. Romanov Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Abstract:
Given a metric space with a Borel measure $\mu$, we consider a class of functions whose increment is controlled by the measure of a ball containing the corresponding points and a nonnegative function $p$-summable with respect to $\mu$. We prove some analogs of the classical theorems on embedding Sobolev function classes into Lebesgue spaces.
Keywords:
metric space, measure, Sobolev class, embedding theorem.
Received: 25.06.2003
Citation:
A. S. Romanov, “Embedding theorems for a certain function class of Sobolev type on metric spaces”, Sibirsk. Mat. Zh., 45:2 (2004), 452–465; Siberian Math. J., 45:2 (2004), 376–387
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https://www.mathnet.ru/eng/smj1081 https://www.mathnet.ru/eng/smj/v45/i2/p452
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Abstract page: | 362 | Full-text PDF : | 134 | References: | 68 |
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