Strichartz inequalities with weights in Morrey-Campanato classes

  1. Barceló Varcárcel, Juan Antonio
  2. Bennett, Jonathan M.
  3. Carbery, Anthony
  4. Vilela Bendaña, María de la Cruz
Revista:
Collectanea mathematica

ISSN: 0010-0757

Año de publicación: 2010

Volumen: 61

Fascículo: 1

Páginas: 49-56

Tipo: Artículo

DOI: 10.1007/BF03191225 DIALNET GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: Collectanea mathematica

Resumen

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.

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Información de financiación

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.

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