### 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 |

Externally published | Yes |

### Fingerprint

### Keywords

- Lorentz spaces
- Schrödinger equation
- Wave operators

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**Existence and mapping properties of the wave operator for the Schrödinger equation with singular potential.** / Gueorguiev, Vladimir Simeonov; Ivanov, Angel.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 133, no. 7, pp. 1993-2003. https://doi.org/10.1090/S0002-9939-05-07854-8

}

TY - JOUR

T1 - Existence and mapping properties of the wave operator for the Schrödinger equation with singular potential

AU - Gueorguiev, Vladimir Simeonov

AU - Ivanov, Angel

PY - 2005/7

Y1 - 2005/7

N2 - We consider the Schrödinger equation in three-dimensional space with small potential in the Lorentz space L3/2,∞ 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 Hs and Hv s in the case 0 ≤ s < 3/2.

AB - We consider the Schrödinger equation in three-dimensional space with small potential in the Lorentz space L3/2,∞ 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 Hs and Hv s in the case 0 ≤ s < 3/2.

KW - Lorentz spaces

KW - Schrödinger equation

KW - Wave operators

UR - http://www.scopus.com/inward/record.url?scp=22544441593&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=22544441593&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-05-07854-8

DO - 10.1090/S0002-9939-05-07854-8

M3 - Article

AN - SCOPUS:22544441593

VL - 133

SP - 1993

EP - 2003

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 7

ER -