Commutator estimates on contact manifolds and applications
Journal article, 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


Heiko Gimperlein

Heriot-Watt University

Padernborn University

Magnus C H T Goffeng

Chalmers, Mathematical Sciences, Analysis and Probability Theory

University of Gothenburg

Journal of Noncommutative Geometry

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

Vol. 13 1 363-406

Subject Categories

Algebra and Logic


Mathematical Analysis


Basic sciences



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