New characterizations of Hajłasz-Sobolev spaces on metric spaces (Q813792)
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scientific article; zbMATH DE number 5005671
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | New characterizations of Hajłasz-Sobolev spaces on metric spaces |
scientific article; zbMATH DE number 5005671 |
Statements
New characterizations of Hajłasz-Sobolev spaces on metric spaces (English)
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13 February 2006
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The author introduces on spaces of homogeneous type \((X, \rho, \mu)\), consisting of a set \(X\), a quasi-metric \(\rho\) and a doubling Borel measure \(\mu\), fractional Sobolev spaces \(W^s_p (X)\) where \(1 \leq p \leq \infty\) and \(s>0\). The paper deals with equivalent characterisations of these spaces in terms of local means and maximal functions.
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Sobolev space
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Lipschitz-type space
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embedding theorem
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maximal function
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space of homogeneous type
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