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Sobolev meets Poincaré. (English. Abridged French version) Zbl 0837.46024
Summary: We prove that a very weak form of the Poincaré inequality implies a Sobolev-Poincaré inequality in the abstract setting of metric spaces.

MSC:
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
54E35 Metric spaces, metrizability
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