On the boundedness of Pseudo-differential operators on Triebel-Lizorkin and Besov spaces

TL;DR

This paper establishes sharp endpoint boundedness results for a class of pseudo-differential operators on Triebel-Lizorkin and Besov spaces, including those with compound symbols.

Contribution

It provides the first sharp endpoint boundedness results for pseudo-differential operators of type (ρ,ρ) on these function spaces, covering operators with compound symbols.

Findings

Endpoint boundedness properties are proven for operators of type (ρ,ρ).

Results are sharp and optimal.

Operators with compound symbols are also included.

Abstract

In this work we show endpoint boundedness properties of pseudo-differential operators of type $(\rho,\rho)$, $0<\rho<1$, on Triebel-Lizorkin and Besov spaces. Our results are sharp and they also cover operators defined by compound symbols.