Geodesic inversion and Sobolev spaces on Heisenberg type groups
Tóm tắt
Let σ be the geodesic inversion on a Heisenberg type groupN with homogeneous dimensionQ, and denote byS the jacobian of σ. We prove that, for
$$ - \frac{1}{2}Q< \alpha< \frac{1}{2}Q$$
, the operators
$$T_\alpha :f \mapsto S^{1/2 - \alpha /Q} (f \circ \sigma )$$
are bounded on certain homogeneous Sobolev spaces
$$\mathcal{H}^\alpha (N)$$
if and only ifN is an IwasawaN-group.
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