### Abstract

We consider the Schrödinger equation in three-dimensional space with small potential in the Lorentz space L^{3/2,∞} and we prove Strichartz-type estimates for the solution to this equation. Moreover, using Cook's method, we prove the existence of the wave operator. In the last section we prove the equivalence between the homogeneous Sobolev spaces H^{s} and H_{v}^{s} in the case 0 ≤ s < 3/2.

Original language | English |
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Pages (from-to) | 1993-2003 |

Number of pages | 11 |

Journal | Proceedings of the American Mathematical Society |

Volume | 133 |

Issue number | 7 |

DOIs | |

Publication status | Published - 2005 Jul 1 |

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### Keywords

- Lorentz spaces
- Schrödinger equation
- Wave operators

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics