An \(L^p\)-spectral multiplier theorem with sharp \(p\)-specific regularity bound on Heisenberg type groups (Q6550711)
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scientific article; zbMATH DE number 7860409
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An \(L^p\)-spectral multiplier theorem with sharp \(p\)-specific regularity bound on Heisenberg type groups |
scientific article; zbMATH DE number 7860409 |
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An \(L^p\)-spectral multiplier theorem with sharp \(p\)-specific regularity bound on Heisenberg type groups (English)
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5 June 2024
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The author considers a group of Heisenberg type and proves a spectral multiplier estimate, and its corresponding result for Bochner-Riesz multipliers. He obtains a sharp regularity condition on the order of the Sobolev space. The method for the proof used relies on restriction type estimates on the multiplier function and a dyadic decompositon on each multiplier restriction along the spectrum of the Laplacian.
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nilpotent Lie group
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Heisenberg type group
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sub-Laplacian
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spectral multiplier
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restriction type estimate
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sub-Riemannian geometry
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