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Generalized Poincaré inequalities: Sharp self-improving properties. (English) Zbl 0903.46029
Let $$(S,d,\mu)$$ be a space of homogeneous type (a set $$S$$ equipped with a quasi-metric $$d$$ and a measure $$\mu$$ satisfying the global doubling condition). The paper deals with abstract Poincaré inequalities and Sobolev embeddings in $$(S,d,\mu)$$.
Reviewer: H.Triebel (Jena)

##### MSC:
 4.6e+36 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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