Elementary Proofs for Kato Smoothing Estimates of Schr\"odinger-like Dispersive Equations

TL;DR

This paper provides elementary proofs of extended and refined Kato smoothing estimates for Schrödinger-like dispersive equations, simplifying the understanding of these classical results.

Contribution

It introduces new elementary methods to extend and refine classical Kato smoothing estimates for dispersive equations.

Findings

Extended Kato estimates with elementary proofs

Refined smoothing estimates for Schrödinger-like equations

Simplified approach to classical dispersive analysis

Abstract

In this expository note, we prove some extensions and refinements of classical Kato type estimates with elementary techniques.