Commutator estimates on contact manifolds and applications

Heiko Gimperlein, Magnus Goffeng

Research output: Contribution to journalArticle

Abstract

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 Calderón commutator estimate: If D is a first-order operator in the Heisenberg calculus and f is Lipschitz in the Carnot–Carathéodory metric, then ŒD; 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 Hölder 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.

Original languageEnglish
Pages (from-to)363-406
Number of pages44
JournalJournal of Noncommutative Geometry
Volume13
Issue number1
DOIs
Publication statusPublished - 11 Mar 2019

Fingerprint

Commutator Estimate
Contact Manifold
Commutator
Schatten Class
Spectral Triples
Multiplication Operator
Zeroth
Bounded Operator
Pseudodifferential Operators
Operator
Lipschitz
Regularization
Continuous Function
Calculus
Interpolate
First-order
Norm
Imply
Metric
Closed

Keywords

  • Commutator estimates
  • Connes metrics
  • Hankel operators
  • Heisenberg calculus
  • Hypoelliptic operators
  • Weak Schatten norm estimates

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Mathematical Physics
  • Geometry and Topology

Cite this

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Commutator estimates on contact manifolds and applications. / Gimperlein, Heiko; Goffeng, Magnus.

In: Journal of Noncommutative Geometry, Vol. 13, No. 1, 11.03.2019, p. 363-406.

Research output: Contribution to journalArticle

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