Hardy-type inequalities for moduli of continuity (Q2714730)
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scientific article; zbMATH DE number 1607212
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Hardy-type inequalities for moduli of continuity |
scientific article; zbMATH DE number 1607212 |
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20 June 2001
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Hardy inequalities
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function spaces
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integral representation theorem
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moduli of continuity
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Hardy-type inequalities for moduli of continuity (English)
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Theorem 2.1 is a new integral representation theorem for functions \(f(x)\) in balls in \({\mathbb R}^n\) in terms of some means of \(f\) and of its differences \(\Delta^k_h f\). This representation theorem is used in Theorems 3.1 and 3.2 to obtain sharp \(n\)-dimensional Hardy inequalities in terms of moduli of continuity with respect to \(f\).NEWLINENEWLINEFor the entire collection see [Zbl 0952.00006].
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