Global and local smoothness of the Hilbert transforms (Q2446179)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Global and local smoothness of the Hilbert transforms |
scientific article |
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Global and local smoothness of the Hilbert transforms (English)
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16 April 2014
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The Hilbert transform is defined as \[ H(f)(x)=(\text{v.p})\int_{\mathbb R} \frac{f(x+t)}{t}\,dt, \] where \(f\) is a measurable function defined on \({\mathbb R}\). The authors study the smoothness properties of the Hilbert transform in terms of the smoothness of the function itself. Furthermore, they prove global and local analogues of Privalov's theorem and show the sharpness of their results.
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Hilbert transforms
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Privalov's Theorem
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global and local smoothness
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