\(L^p\)-boundedness of the wave operator for the one dimensional Schrödinger operator
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Publication:996037
DOI10.1007/S00220-006-0098-XzbMATH Open1127.35053arXivmath-ph/0509059OpenAlexW2161770094MaRDI QIDQ996037
Author name not available (Why is that?)
Publication date: 11 September 2007
Published in: (Search for Journal in Brave)
Abstract: Given a one dimensional perturbed Schroedinger operator H=-(d/dx)^2+V(x) we consider the associated wave operators W_+, W_- defined as the strong L^2 limits as s-> pminfty of the operators e^{isH} e^{-isH_0} We prove that the wave operators are bounded operators on L^p for all 1<p<infty, provided (1+|x|)^2 V(x) is integrable, or else (1+|x|)V(x) is integrable and 0 is not a resonance. For p=infty we obtain an estimate in terms of the Hilbert transform. Some applications to dispersive estimates for equations with variable rough coefficients are given.
Full work available at URL: https://arxiv.org/abs/math-ph/0509059
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