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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:
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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