A sharp uncertainty principle and Hardy-Poincaré inequalities on sub-Riemannian manifolds (Q2885365)
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scientific article; zbMATH DE number 6037652
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A sharp uncertainty principle and Hardy-Poincaré inequalities on sub-Riemannian manifolds |
scientific article; zbMATH DE number 6037652 |
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A sharp uncertainty principle and Hardy-Poincaré inequalities on sub-Riemannian manifolds (English)
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23 May 2012
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Hardy-Poincaré inequality
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uncertainty principle
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sub-Riemannian manifold
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The authors proves a sharp Heisenberg uncertainty principle inequality and Hardy-Poincaré inequality on the sub-Riemannian manifold \(\mathbb R^{2n+1}\) defined by the vector fields: NEWLINE\[NEWLINE X_j=\frac{\partial}{\partial x_j}+2ky_j|z|^{2k-2} \frac{\partial}{\partial l}, \qquad j=1,2,\ldots, n NEWLINE\]NEWLINE where \(|z|=(|x|^2+|y|^2)^{1/2}\) and \(k\geq 1.\)
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