The 𝑊^{𝑠,𝑝}-boundedness of stationary wave operators for the Schrödinger operator with inverse-square potential

DOI10.1090/tran/8823OpenAlexW4311082229MaRDI QIDQ5878210

Xiaoyan Su, Ji Qiang Zheng, Chang Xing Miao

Publication date: 20 February 2023

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2110.01969

zbMATH Keywords

Schrödinger operatormultiplier theoreminverse-square potentialdispersive estimatelocal smoothing estimateuniform Sobolev inequalityequivalence of Sobolev normsstationary wave operator

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Schrödinger operator, Schrödinger equation (35J10) Classical hypergeometric functions, ({}_2F_1) (33C05) Operator theory (47-XX)

Related Items (3)

Scattering of the focusing energy-critical NLS with inverse square potential ⋮ On Sobolev norms involving Hardy operators in a half-space ⋮ Scattering threshold for a focusing inhomogeneous non-linear Schrödinger equation with inverse square potential

Uses Software

• DLMF

Cites Work

• Time decay of scaling critical electromagnetic Schrödinger flows
• Scattering theory for nonlinear Schrödinger equations with inverse-square potential
• The energy-critical NLS with inverse-square potential
• Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators
• Propagation of singularities and maximal functions in the plane
• Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
• Strichartz estimates for the wave and Schrödinger equations with the inverse-square potential
• Non trivial \(L^q\) solutions to the Ginzburg-Landau equation
• The Hardy inequality and the asymptotic behaviour of the heat equation with an inverse-square potential
• Scattering in \(H^{1}\) for the intercritical NLS with an inverse-square potential
• Sobolev spaces adapted to the Schrödinger operator with inverse-square potential
• \(L^p\) estimates for the wave equation with the inverse-square potential
• \(L^p\)-boundedness of wave operators for two-dimensional Schrödinger operators
• Remarks on endpoint Strichartz estimates for Schrödinger equations with the critical inverse-square potential
• Uniform Sobolev estimates for Schrödinger operators with scaling-critical potentials and applications
• Uniform resolvent estimates for Schrödinger operator with an inverse-square potential
• The energy-critical nonlinear wave equation with an inverse-square potential
• Time decay of scaling invariant electromagnetic Schrödinger equations on the plane
• The focusing cubic NLS with inverse-square potential in three space dimensions.
• On the order derivatives of Bessel functions
• The abstract theory of scattering
• Existence and asymptotic behavior of standing waves of the nonlinear Helmholtz equation in the plane
• The asymptotic expansion of a ratio of gamma functions
• Fourier Integrals in Classical Analysis
• Structure formulas for wave operators
• Endpoint Strichartz estimates
• Riesz Transforms Outside a Convex Obstacle
• Focusing NLS with inverse square potential
• Uniform resolvent and Strichartz estimates for Schrödinger equations with critical singularities
• Sommes De Cesaro Et Multiplicateurs Des Developpements en Harmoniques Spheriques
• Scattering theory in homogeneous Sobolev spaces for Schrödinger and wave equations with rough potentials
• Strichartz estimates for the wave and Schroedinger equations with potentials of critical decay
• The \(W^{k,p}\)-continuity of wave operators for Schrödinger operators
• The \(W^{k,p}\)-continuity of wave operators for Schrödinger operators
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