Isoperimetric Hardy type and Poincaré inequalities on metric spaces. (English) Zbl 1195.46035
Laptev, Ari (ed.), Around the research of Vladimir Maz’ya. I. Function spaces. Dordrecht: Springer; Novosibirsk: Tamara Rozhkovskaya Publisher (ISBN 978-1-4419-1340-1/hbk; 978-1-4419-1341-8/ebook; 978-5-9018-7341-0/hbk). International Mathematical Series (New York) 11, 285-298 (2010).
Summary: We give a general construction of manifolds for which Hardy type operators characterize Poincaré inequalities. We also show a class of spaces where this property fails. As an application, we extend recent results of E.Milman to our setting.
For the entire collection see [Zbl 1180.47001].
For the entire collection see [Zbl 1180.47001].
MSC:
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
| 30L99 | Analysis on metric spaces |
| 58J99 | Partial differential equations on manifolds; differential operators |
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