Strichartz inequalities with weights in Morrey-Campanato classes
- Barceló Varcárcel, Juan Antonio
- Bennett, Jonathan M.
- Carbery, Anthony
- Vilela Bendaña, María de la Cruz
ISSN: 0010-0757
Année de publication: 2010
Volumen: 61
Fascículo: 1
Pages: 49-56
Type: Article
D'autres publications dans: Collectanea mathematica
Résumé
We prove some weighted refinements of the classical Strichartz inequalities for initial data in the Sobolev spaces $H^s (R^n)$. We control the weighted $L^2$ �norm of the solution of the free Schrödinger equation when the weight is in a Morrey�Campanato type space adapted to that equation. Our partial positive results are complemented by some necessary conditions based on estimates for certain particular solutions of the free Schrödinger equation.
Information sur le financement
The first and fourth authors were supported by Spanish Grant MTM2008-02568, the fifth by Spanish Grant MTM2007-62186, the second by EPSRC Grant EP/E022340/1 and the third by EC project “Pythagoras II” and a Leverhulme Study Abroad Fellowship.Financeurs
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Engineering and Physical Sciences Research Council
United Kingdom
- EP/E022340/1
- European Commission European Union