Necessary conditions for the \(L^{p}\)-convergence \((0<p<1)\) of single and double trigonometric series. (Q2925942)
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scientific article; zbMATH DE number 6362243
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Necessary conditions for the \(L^{p}\)-convergence \((0<p<1)\) of single and double trigonometric series. |
scientific article; zbMATH DE number 6362243 |
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29 October 2014
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trigonometric series
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Hardy-Littlewood inequality for functions in \(H^{p}\)
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Bernstein-Zygmund inequalities for the derivative of trigonometric polynomials in \(L^{p}\)-metric for \(0<p<1\)
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necessary conditions for the convergence in \(L^{p}\)-metric
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Necessary conditions for the \(L^{p}\)-convergence \((0<p<1)\) of single and double trigonometric series. (English)
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In this paper necessary conditions in terms of the coefficients for the convergence of a double trigonometric series in the \(L^p\)-metric (\(0<p<1\)) are given. The authors succeed to obtain valuable results. In the proofs they use the Hardy-Littlewood inequality for functions in \(H^p\) and the Bernstein-Zygmund inequalities for the derivatives of trigonometric polynomials and their conjugates in the \(L^p\)-metric (\(0<p<1\)).
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