Existence and mapping properties of the wave operator for the Schrödinger equation with singular potential期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	Vladimir Georgiev Angel Ivanov

Affiliation:	Dipartimento di Matematica, Università di Pisa, Via Buonarroti No.2, 56127 - Pisa, Italy ; Dipartimento di Matematica, Università di Pisa, Via Buonarroti No.2, 56127 - Pisa, Italy

Abstract:	We consider the Schrödinger equation in three-dimensional space with small potential in the Lorentz space $L^{3/2,infty}$ 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 $dot{H}^s$ and $dot{H}^s_V$ in the case $0 leq s < frac{3}{2}$ .

Keywords:	Schr" {o}dinger equation, Lorentz spaces, wave operators

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