On summation of Fourier coefficients by Hölder (H,k) methods (Q804871)
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scientific article; zbMATH DE number 4203002
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On summation of Fourier coefficients by Hölder (H,k) methods |
scientific article; zbMATH DE number 4203002 |
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On summation of Fourier coefficients by Hölder (H,k) methods (English)
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1990
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The author proves that if \(f(t)\in L_ p[0,2\pi]\), where \(p\in (1,+\infty)\), then \(n^{1-1/p}\cdot a_ n\to 0\) as \(n\to \infty\) in the \((H,1)\) sense. (Here \(a_ n=(1/\pi)\int^{2\pi}_{0}f(t)\cos nt\quad dt,\quad n=0,1,2...\).)
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summation by Hölder methods
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Fourier coefficients
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