Multilinear pseudo-differential operators with $S_{0,0}$ class symbols of limited smoothness

TL;DR

This paper investigates the boundedness of multilinear pseudo-differential operators with symbols in the $S_{0,0}$ class, focusing on the smoothness conditions needed for boundedness between local Hardy spaces.

Contribution

It establishes new smoothness criteria for symbols in the $S_{0,0}$ class to ensure boundedness of multilinear pseudo-differential operators on local Hardy spaces.

Findings

Derived sufficient smoothness conditions for boundedness

Extended boundedness results to multilinear operators

Clarified the role of symbol smoothness in operator boundedness

Abstract

We consider the boundedness of the multilinear pseudo-differential operators with symbols in the multilinear H\"{o}rmander class $S_{0,0}$. The aim of this paper is to discuss smoothness conditions for symbols to assure the boundedness between local Hardy spaces.