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 Hvs in the case 0 ≤ s < 3/2.
ASJC Scopus subject areas
- 数学 (全般)