Deformations of the \(Z(\omega_2; L(T^m))\) classes (Q2709536)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Deformations of the \(Z(\omega_2; L(T^m))\) classes |
scientific article |
Statements
23 January 2002
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conjugate function
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Zygmund's condition
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second difference
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Deformations of the \(Z(\omega_2; L(T^m))\) classes (English)
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Theorems of I. Privalov and Hardy-Littlewood are well known which state the invariance of \(\text{Lip }\alpha,\) \(0<\alpha<1,\) functions under the conjugation operator, when the \(\alpha\) smoothness is measured in \(C\) or \(L,\) respectively. In the case \(\alpha=1\) such results are no more valid, but Zygmund's result holds in which the second difference is used to define smoothness. In the paper under review the latter result is partially generalized to the multivariate case.
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