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


Authors: Valentina Casarino and Marco M. Peloso
Journal: Trans. Amer. Math. Soc. 367 (2015), 2631-2664
MSC (2010): Primary 35Q41; Secondary 43A85, 35B65, 33C55
DOI: https://doi.org/10.1090/S0002-9947-2014-06162-X
Published electronically: July 24, 2014
MathSciNet review: 3301876
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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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Additional Information

Valentina Casarino
Affiliation: DTG, Università degli Studi di Padova, Stradella san Nicola 3, I-36100 Vicenza, Italy
Email: valentina.casarino@unipd.it

Marco M. Peloso
Affiliation: Dipartimento di Matematica, Università degli Studi di Milano, Via C. Saldini 50, I-20133 Milano, Italy
Email: marco.peloso@unimi.it

DOI: https://doi.org/10.1090/S0002-9947-2014-06162-X
Keywords: Schr\"odinger equation, Strichartz estimates, complex spheres, sublaplacian, dispersive estimates.
Received by editor(s): January 25, 2013
Published electronically: July 24, 2014
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.