Boundedness of pseudo-differential operators of type (0,0) on Triebel-Lizorkin and Besov spaces

TL;DR

This paper proves precise boundedness conditions for certain pseudo-differential operators on Triebel-Lizorkin and Besov function spaces, advancing understanding of their behavior in harmonic analysis.

Contribution

It establishes sharp boundedness results for pseudo-differential operators of type (0,0) on Triebel-Lizorkin and Besov spaces, which was previously not fully understood.

Findings

Sharp boundedness results for operators on $F_p^{s,q}$ and $B_p^{s,q}$ spaces.

Conditions under which these operators are bounded are precisely characterized.

The results improve upon previous bounds and extend the theory of pseudo-differential operators.

Abstract

In this work we establish sharp boundedness results for pseudo-differential operators corresponding to $a\in\mathcal{S}_{0,0}^{m}$ on Triebel-Lizorkin spaces $F_p^{s,q}$ and Besov spaces $B_p^{s,q}$.