Abstract
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.
| Original language | English |
|---|---|
| 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 |
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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.
In: Proceedings of the American Mathematical Society, Vol. 133, No. 7, 07.2005, p. 1993-2003.Research output: Contribution to journal › Article
}
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
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 -