Norm inequalities for potential-type operators in homogeneous spaces (Q2748469)
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scientific article; zbMATH DE number 1659515
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Norm inequalities for potential-type operators in homogeneous spaces |
scientific article; zbMATH DE number 1659515 |
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14 July 2002
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Borel measures
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homogeneous spaces
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trace inequalities
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Wolff potential
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Norm inequalities for potential-type operators in homogeneous spaces (English)
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The authors give a characterization of positive Borel measures \(\mu\) on a homogeneous space \(X\) (in the sense of Coifman and Weiss) satisfying the trace inequality NEWLINE\[NEWLINE\Biggl( \int_X (I_\varphi* f)^q(x) \mu(dx)\Biggr)^{1/q}\leq C\Biggl( \int_X|f(x)|^p \sigma(dx)\Biggr)^{1/p}NEWLINE\]NEWLINE where \(f\geq 0\), \(I_\varphi(x)\) is a certain generalized Riesz kernel on \(X\), \(1\leq q< p<\infty\), and \(\sigma\) is the measure on \(X\) having the doubling property.
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