Abstract
Given a metric space with a Borel measure μ, 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 μ. We prove some analogs of the classical theorems on embedding Sobolev function classes into Lebesgue spaces.
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Romanov, A.S. Embedding Theorems for a Certain Function Class of Sobolev Type on Metric Spaces. Siberian Mathematical Journal 45, 376–387 (2004). https://doi.org/10.1023/B:SIMJ.0000021292.79527.b5
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DOI: https://doi.org/10.1023/B:SIMJ.0000021292.79527.b5