Sine, cosine transforms and classical function classes (Q624180)
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scientific article; zbMATH DE number 5848525
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Sine, cosine transforms and classical function classes |
scientific article; zbMATH DE number 5848525 |
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Sine, cosine transforms and classical function classes (English)
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8 February 2011
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For Fourier series with positive coefficients, it was known [\textit{R. P. jun. Boas}, J. Math. Anal. Appl. 17, 463--483 (1967; Zbl 0154.06102); \textit{F. Móricz}, Anal. Math. 34, No.~4, 261--276 (2008; Zbl 1199.42028)] that the membership to \(\alpha\)-Lipschitz classes (resp., \(\alpha\)-Zygmund classes) is equivalent to the decay \(\sum_{k=0}^n ka_k=O\big(n^{1-\alpha}\big) \) (resp., \(\sum_{k=0}^n k^2a_k=O\big(n^{2-\alpha}\big)\)). The author proves the corresponding results in the framework of the real line.
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