Scaling-sharp dispersive estimates for the Korteweg-de Vries group

TL;DR

This paper establishes scaling-sharp weighted estimates for the linear KdV group, providing tools that could be useful for analyzing small data scattering in generalized KdV equations.

Contribution

It introduces new weighted estimates for the linear KdV group that are sharp with respect to scaling, advancing the mathematical understanding of dispersive PDEs.

Findings

Proved weighted estimates on the linear KdV group

Estimates are sharp with respect to scaling

Potential applications to small data scattering in generalized KdV equations

Abstract

We prove weighted estimates on the linear KdV group, which are scaling sharp. This kind of estimates are in the spirit of that used to prove small data scattering for the generalized KdV equations.