Summability of Fourier transforms and absolute convergence of multiple Fourier series (Q1813235)
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scientific article; zbMATH DE number 5835
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Summability of Fourier transforms and absolute convergence of multiple Fourier series |
scientific article; zbMATH DE number 5835 |
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Summability of Fourier transforms and absolute convergence of multiple Fourier series (English)
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25 June 1992
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Applying Hausdorff-Young inequality for multiple Fourier transforms and Fourier series in spaces \(L_ q\) with mixed powers \(q=(q_ 1,\ldots,q_ n)\), there are obtained estimations of \(L_ q\)-norms \((l_ q\)-norms) of Fourier transforms (sequences of Fourier coefficients) by means of integral moduli of continuity with multipower \(p=(p_ 1,\ldots,p_ n)\) conjugate to \(q\).
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spaces \(L^ p\)
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multiple Fourier series
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absolute convergence
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Hausdorff-Young inequality
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multiple Fourier transform
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