Commutator estimates on contact manifolds and applications

Heiko Gimperlein, Magnus Goffeng

Research output: Contribution to journalArticle

1 Citation (Scopus)
40 Downloads (Pure)

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

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

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