Geodesic inversion and Sobolev spaces on Heisenberg type groupsArkiv för Matematik - Tập 43 - Trang 51-67 - 2005
Francesca Astengo, Bianca Di Blasio
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.... hiện toàn bộ