Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Improved local smoothing estimate for the fractional Schrödinger operator

Chuanwei Gao, Changxing Miao, Jiqiang Zheng

Abstract

In this paper, we consider the local smoothing estimate of fractional Schrödinger operator $e^{it(-Δ)^{α/2}}$ with $α>1$. Using the $k$-broad "norm" estimate developed by Guth, we improve the previous best results of local smoothing estimate for the fractional Schrödinger operator .

Improved local smoothing estimate for the fractional Schrödinger operator

Abstract

In this paper, we consider the local smoothing estimate of fractional Schrödinger operator with . Using the -broad "norm" estimate developed by Guth, we improve the previous best results of local smoothing estimate for the fractional Schrödinger operator .

Paper Structure

This paper contains 4 sections, 10 theorems, 102 equations.

Table of Contents

  1. introduction
  2. preliminaries
  3. Proof of Theorem \ref{['theoa1']}
  4. appendix

Key Result

Theorem 1.2

Let $\alpha>1$, $n\ge 1$ and $s>s_{\alpha,p}-\frac{\alpha}{p}$ with Then

Theorems & Definitions (18)

  • Conjecture 1.1: Local smoothing for the fractional Schrödinger operator
  • Theorem 1.2
  • Remark 1.3
  • Definition 2.1: Elliptic phase functions
  • Lemma 2.2
  • proof
  • Corollary 2.3
  • proof
  • Lemma 2.4
  • Theorem 3.1: GHI
  • ...and 8 more