A sharpness result for powers of Besov functions (Q1769310)
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scientific article; zbMATH DE number 2147911
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A sharpness result for powers of Besov functions |
scientific article; zbMATH DE number 2147911 |
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A sharpness result for powers of Besov functions (English)
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21 March 2005
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Summary: A recent result of Kateb asserts that \(f\in B^s_{p,q} (\mathbb{R}^n)\) implies \(|f|^\mu\in B^s_{p,q}(\mathbb{R}^n)\) as soon as the following three conditions hold (1) \(0<s<\mu+(1/p)\), (2) \(f\) is bounded, (3) \(\mu >1\). By means of counterexamples, we prove that these conditions are optimal.
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