• Corpus ID: 237491963

A note on local smoothing estimates for fractional Schr\"{o}dinger equations

@inproceedings{Gan2021ANO,
  title={A note on local smoothing estimates for fractional Schr\"\{o\}dinger equations},
  author={Shengwen Gan and Changkeun Oh and Shukun Wu},
  year={2021}
}
. We improve local smoothing estimates for fractional Schr¨odinger equations for α ∈ (0 , 1) ∪ (1 , ∞ ). 
[PDF] Semantic Reader
4 Citations
Background Citations
1

4 Citations

New bounds for Stein's square functions in higher dimensions

We improve the L(R) bounds on Stein’s square function to the best known range of the Fourier restriction problem when n ≥ 4. Applications including certain local smoothing estimates are also…

Local smoothing estimates of fractional Schrödinger equations in $$\alpha $$-modulation spaces with some applications

  • Yufeng Lu
  • Mathematics
    Journal of Evolution Equations
  • 2023
We show some new local smoothing estimates of the fractional Schr\"odinger equations with initial data in $\alpha$-modulation spaces via decoupling inequalities. Furthermore, our necessary conditions…

A type of oscillatory integral operator and its applications

In this paper, we consider Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}…

Sharp endpoint $L_p$ estimates of quantum Schr\"{o}dinger groups

A bstract . In this article, we establish sharp endpoint L p estimates of Schr¨odinger groups on general measure spaces which may not be equipped with good metrics but admit submarkovian semigroups…

20 References

New bounds for Stein's square functions in higher dimensions

We improve the L(R) bounds on Stein’s square function to the best known range of the Fourier restriction problem when n ≥ 4. Applications including certain local smoothing estimates are also…

A Restriction Estimate for Surfaces with Negative Gaussian Curvatures

We prove $L^p$ bounds for the Fourier extension operators associated to surfaces in $\mathbb{R}^3$ with negative Gaussian curvatures for every $p>3.25$.

Endpoint maximal and smoothing estimates for Schrödinger equations

Abstract For α > 1 we consider the initial value problem for the dispersive equation i∂tu + (–Δ) α/2 u = 0. We prove an endpoint Lp inequality for the maximal function with initial values in Lp…

A note on Fourier restriction and nested Polynomial Wolff axioms

This note records an asymptotic improvement on the known $L^p$ range for the Fourier restriction conjecture in high dimensions. This is obtained by combining Guth's polynomial partitioning method…

A local smoothing estimate for the Schrödinger equation

Improved local smoothing estimates for the fractional Schrödinger operator

In this paper, we consider local smoothing estimates for the fractional Schrödinger operator eit(−Δ)α/2$e^{it(-\Delta )^{\alpha /2}}$ with α>1$\alpha >1$ . Using the k$k$ ‐broad ‘norm’ estimates of…

Restriction estimates using polynomial partitioning II

We improve the estimates in the restriction problem in dimension $n \ge 4$. To do so, we establish a weak version of a $k$-linear restriction estimate for any $k$. The exponents in this weak…

Fourier restriction for smooth hyperbolic 2-surfaces

We prove Fourier restriction estimates by means of the polynomial partitioning method for compact subsets of any sufficiently smooth hyperbolic hypersurface in $$\mathbb {R}^3.$$ R 3 .…

Sharp variation-norm estimates for oscillatory integrals related to Carleson’s theorem

We prove variation-norm estimates for certain oscillatory integrals related to Carleson's theorem. Bounds for the corresponding maximal operators were first proven by Stein and Wainger. Our estimates…

Bounds on Oscillatory Integral Operators Based on Multilinear Estimates

We apply the Bennett–Carbery–Tao multilinear restriction estimate in order to bound restriction operators and more general oscillatory integral operators. We get improved Lp estimates in the Stein…