Fourier transform is an isometry on some weighted Sobolev spaces (Q387852)
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scientific article; zbMATH DE number 6238893
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fourier transform is an isometry on some weighted Sobolev spaces |
scientific article; zbMATH DE number 6238893 |
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Fourier transform is an isometry on some weighted Sobolev spaces (English)
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17 December 2013
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Fourier transform
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weighted Sobolev space
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isometry
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invariant space
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Plancherel identity
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It is shown that, under adequate norms, the Fourier transform is an isometry over a chain of nested weighted Sobolev spaces. Precisely, NEWLINE\[NEWLINE {\mathcal F}(W^{r,p}_s)\hookrightarrow W^{s,p^*}_r. NEWLINE\]NEWLINE As a result, an infinite number of useful Plancherel-like identities are derived. Possible extensions are discussed, giving rise to some open questions.
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