A local smoothing estimate for the Schrödinger equation
From MaRDI portal
Publication:952436
DOI10.1016/J.AIM.2008.08.008zbMath1157.35326OpenAlexW2018250680MaRDI QIDQ952436
Publication date: 12 November 2008
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.aim.2008.08.008
Asymptotic behavior of solutions to PDEs (35B40) A priori estimates in context of PDEs (35B45) Initial value problems for linear higher-order PDEs (35G10)
Related Items (24)
Transference of local to global \(L^{2}\) maximal estimates for dispersive partial differential equations ⋮ Linear adjoint restriction estimates for paraboloid ⋮ A sharp regularity estimate for the Schrödinger propagator on the sphere ⋮ A sharp Schrödinger maximal estimate in \(\mathbb{R}^2\) ⋮ Global range estimates for maximal oscillatory integrals with radial test functions ⋮ A note on local smoothing estimates for fractional Schrödinger equations ⋮ Pointwise convergence of sequential Schrödinger means ⋮ Maximal estimate for solutions to a class of dispersive equation with radial initial value ⋮ Fourier restriction estimates on quantum Euclidean spaces ⋮ On smoothing estimates for Schrödinger equations on product spaces \(\mathbb{T}^m \times \mathbb{R}^n\) ⋮ A counterexample to the global dual \(L^3\) Schrödinger maximal estimate in \(\mathbb{R}^2\) ⋮ Local smoothing estimates of fractional Schrödinger equations in \(\alpha\)-modulation spaces with some applications ⋮ Improved local smoothing estimates for the fractional Schrödinger operator ⋮ Sharp variation-norm estimates for oscillatory integrals related to Carleson's theorem ⋮ Space-time estimates on damped fractional wave equation ⋮ Endpoint maximal and smoothing estimates for Schrödinger equations ⋮ Maximal Function Estimates and Local Well-Posedness for the Generalized Zakharov--Kuznetsov Equation ⋮ Coherence on fractals versus pointwise convergence for the Schrödinger equation ⋮ Local smoothing estimates for some half-wave operators ⋮ An improved maximal inequality for 2D fractional order Schrödinger operators ⋮ Unnamed Item ⋮ Global maximal inequality to a class of oscillatory integrals ⋮ On smoothing estimates in modulation spaces and the nonlinear Schrödinger equation with slowly decaying initial data ⋮ A type of oscillatory integral operator and its applications
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Improved bounds for Bochner-Riesz and maximal Bochner-Riesz operators
- The boundedness of the maximal Bochner-Riesz operator on \(L^ 4\)(\(R^ 2\))
- Regularity of solutions to the Schrödinger equation
- \(L^p\) estimates for the waves equation
- Propagation of singularities and maximal functions in the plane
- Wave front sets, local smoothing and Bourgain's circular maximal theorem
- A local smoothing estimate in higher dimensions.
- A sharp bilinear restriction estimate for paraboloids
- Local smoothing type estimates on \(L^p\) for large \(p\)
- Restriction theorems for a surface with negative curvature
- A remark on Schrödinger operators
- A sharp bilinear cone restriction estimate
- Restriction theorems and maximal operators related to oscillatory integrals in \(\mathbf R^3\)
- A bilinear approach to cone multipliers. II: Applications
- \(H^p\) spaces of several variables
- A note on spherical summation multipliers
- A Strong Type (2,2) Estimate for a Maximal Operator Associated to the Schrodinger Equation
- Pointwise convergence of solutions to the nonelliptic Schr\"odinger equation
- Pointwise convergence of solutions to Schr\"odinger equations
- Schrodinger Equations: Pointwise Convergence to the Initial Data
- Local Smoothing Properties of Dispersive Equations
- Well-Posedness of the Initial Value Problem for the Korteweg-de Vries Equation
- Restriction implies Bochner–Riesz for paraboloids
- A counter-example concerning maximal estimates for solutions to equations of Schrodinger type
- Global maximal estimates for solutions to the Schrödinger equation
- Bilinear restriction estimates for surfaces with curvatures of different signs
This page was built for publication: A local smoothing estimate for the Schrödinger equation
