Collectanea mathematica

, Volume 61, Issue 1, pp 49–56 | Cite as

Strichartz inequalities with weights in Morrey-Campanato classes

  • J. A. Barceló
  • J. M. Bennett
  • A. Carbery
  • A. Ruiz
  • M. C. Vilela


We prove some weighted refinements of the classical Strichartz inequalities for initial data in the Sobolev spaces Ḣ s (ℝ n ). We control the weightedL 2-norm of the solution of the free Schrödinger equation whenever 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.


Schrodinger equations Morrey-Campanato Spaces 


34A12 42B35 


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Copyright information

© Universitat de Barcelona 2010

Authors and Affiliations

  • J. A. Barceló
    • 1
  • J. M. Bennett
    • 2
  • A. Carbery
    • 3
  • A. Ruiz
    • 4
  • M. C. Vilela
    • 5
  1. 1.ETSI de CaminosUniversidad Politécnica de MadridMadridSpain
  2. 2.School of MathematicsUniversity of BirminghamBirminghamEngland
  3. 3.School of Mathematics and Maxwell Institute for Mathematical SciencesUniversity of EdinburghEdinburghScotland
  4. 4.Departamento de MatemáticasUniversidad Autónoma de MadridMadridSpain
  5. 5.Departamento de Matemática AplicadaUniversidad de ValladolidSegoviaSpain

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