Commutator estimates on contact manifolds and applications
Artikel i vetenskaplig tidskrift, 2019

This article studies sharp norm estimates for the commutator of pseudo-differential operators with multiplication operators on closed Heisenberg manifolds. In particular, we obtain a Calderon commutator estimate: If D is a first-order operator in the Heisenberg calculus and f is Lipschitz in the Carnot-Caratheodory metric, then [D, f] extends to an L-2-bounded operator. Using interpolation, it implies sharp weak-Schatten class properties for the commutator between zeroth order operators and Holder continuous functions. We present applications to sub-Riemannian spectral triples on Heisenberg manifolds as well as to the regularization of a functional studied by Englis-Guo-Zhang.

Heisenberg calculus

weak Schatten norm estimates

hypoelliptic operators

Hankel operators

Commutator estimates

Connes metrics

Författare

Heiko Gimperlein

Heriot-Watt University

Universität Paderborn

Magnus C H T Goffeng

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Göteborgs universitet

Journal of Noncommutative Geometry

1661-6952 (ISSN) 1661-6960 (eISSN)

Vol. 13 1 363-406

Ämneskategorier

Algebra och logik

Geometri

Matematisk analys

Fundament

Grundläggande vetenskaper

DOI

10.4171/JNCG/326

Mer information

Senast uppdaterat

2019-07-15