Fourier coefficients of characteristic functions of intervals with respect to a complete orthonormal system bounded in \(L^p([0,1])\), \(2<p<\infty\) (Q2352619)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fourier coefficients of characteristic functions of intervals with respect to a complete orthonormal system bounded in \(L^p([0,1])\), \(2<p<\infty\) |
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Fourier coefficients of characteristic functions of intervals with respect to a complete orthonormal system bounded in \(L^p([0,1])\), \(2<p<\infty\) (English)
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3 July 2015
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Main result: for any orthonormal system \(\{\phi_j\}_{j=1}^{\infty}\) which is complete in \(L^2([0,1])\) and uniformly bounded in \(L^p([0,1]),2<p<\infty,\) there exists \(x\in (0,1]\) such that \[ \sum_{j=1}^{\infty}\left|\int_0^x\phi_j(t)dt\right|^{(p-2)/(p-1)}=\infty. \]
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complete orthonormal system
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characteristic functions of intervals
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Haar system
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Fourier coefficients
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spaces \(L^p([0,1])\), \(2< p< \infty\)
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Hölder's inequality
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