$H_\infty$-calculus for Hypoelliptic Pseudodifferential Operators

TL;DR

This paper proves that a broad class of hypoelliptic pseudodifferential operators on R^n and closed manifolds admit a bounded $H_$-calculus, enhancing the functional calculus framework for these operators.

Contribution

It establishes the bounded $H_$-calculus for hypoelliptic pseudodifferential operators, extending previous results to more general classes.

Findings

Bounded $H_$-calculus exists for hypoelliptic pseudodifferential operators

Results apply to operators on R^n and closed manifolds

Enhances analytical tools for hypoelliptic operators

Abstract

We establish the existence of a bounded $H_\infty$-calculus for a large class of hypoelliptic pseudodifferential operators on R^n and closed manifolds.