Strichartz estimates for the Schrödinger equation for the sublaplacian on complex spheres

Casarino, Valentina; Peloso, Marco

doi:10.1090/S0002-9947-2014-06162-X

Strichartz estimates for the Schrödinger equation for the sublaplacian on complex spheres
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by Valentina Casarino and Marco M. Peloso PDF

Trans. Amer. Math. Soc. 367 (2015), 2631-2664 Request permission

Abstract:

In this paper we consider the sublaplacian $\mathcal L$ on the unit complex sphere $S^{2n+1}\subset {\mathbf {C}}^{n+1}$, equipped with its natural CR structure, and derive Strichartz estimates with fractional loss of derivatives for the solutions of the free Schrödinger equation associated with $\mathcal L$. Our results are stated in terms of certain Sobolev-type spaces that measure the regularity of functions on $S^{2n+1}$ differently according to their spectral localization. Stronger conclusions are obtained for particular classes of solutions, corresponding to initial data whose spectrum is contained in a proper cone of ${\mathbf {N}}^2$.

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