A sharp sparse domination of pseudodifferential operators

TL;DR

This paper establishes a precise sparse domination framework for pseudodifferential operators with Hörmander class symbols, enabling new boundedness results on weighted Besov spaces and advancing the understanding of dispersive equations.

Contribution

It introduces a sharp sparse domination approach for pseudodifferential operators with Hörmander class symbols, linking to dispersive equations and weighted Besov space boundedness.

Findings

Sharp sparse domination of pseudodifferential operators.

Boundedness results on weighted Besov spaces.

Application to fundamental solutions of dispersive equations.

Abstract

In this paper, we give a sharp sparse domination of pseudodifferential operators associated with symbols belonging to the H\"{o}rmander class, and fundamental solutions of dispersive equations. Furthermore, we give boundedness results of these operators on weighted Besov spaces by using the sparse domination.