On homogeneous Besov spaces for \(1D\) Hamiltonians without zero resonance

DOI10.1016/j.matpur.2017.07.007zbMath1387.35511arXiv1605.02581OpenAlexW2964048424WikidataQ114148665 ScholiaQ114148665MaRDI QIDQ1689518

Vladimir Georgiev, Anna Rita Giammetta

Publication date: 12 January 2018

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.02581

zbMATH Keywords

elliptic estimatesPaley-Littlewood decompositionequivalent Besov normshomogeneous Besov normsLaplace operator with potential

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) PDEs in connection with quantum mechanics (35Q40) PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables) (35R15) Harmonic analysis and PDEs (42B37)

Cites Work

• Spectral multipliers for Schrödinger operators
• \(L^p\)-boundedness of the wave operator for the one dimensional Schrödinger operator
• Geometric theory of semilinear parabolic equations
• The analysis of linear partial differential operators. II: Differential operators with constant coefficients
• The \(W_{k,p}\)-continuity of the Schrödinger wave operators on the line
• \(L^p\)-\(L^{\acute p}\) estimates for the Schrödinger equation on the line and inverse scattering for the nonlinear Schrödinger equation with a potential
• Sectorial Hamiltonians without zero resonance in one dimension
• Inverse scattering on the line
• Decay and Scattering of Small Solutions of Pure Power NLS in ℝ with p > 3 and with a Potential
• Scattering theory
• The \(W^{k,p}\)-continuity of wave operators for Schrödinger operators
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