Commutator estimates on contact manifolds and applications
(2019) In Journal of Noncommutative Geometry 13(1). p.363-406- 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 [D,f] extends to an L^2-bounded operator. Using interpolation, it implies sharpweak-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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/9aa4a902-38c7-4ebc-88ed-7d74b201620b
- author
- Goffeng, Carl Henrik Tryggve Magnus LU and Gimperlein, Heiko
- publishing date
- 2019
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Commutator estimates, Heisenberg calculus, hypoelliptic operators, weak Schatten norm estimates, Hankel operators, Connes metrics
- in
- Journal of Noncommutative Geometry
- volume
- 13
- issue
- 1
- pages
- 363 - 406
- publisher
- European Mathematical Society Publishing House
- external identifiers
-
- scopus:85064332790
- ISSN
- 1661-6960
- DOI
- 10.4171/JNCG/326
- language
- English
- LU publication?
- no
- id
- 9aa4a902-38c7-4ebc-88ed-7d74b201620b
- date added to LUP
- 2021-03-12 11:53:44
- date last changed
- 2022-04-27 00:48:34
@article{9aa4a902-38c7-4ebc-88ed-7d74b201620b, 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 [D,f] extends to an L^2-bounded operator. Using interpolation, it implies sharpweak-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.}}, author = {{Goffeng, Carl Henrik Tryggve Magnus and Gimperlein, Heiko}}, issn = {{1661-6960}}, keywords = {{Commutator estimates; Heisenberg calculus; hypoelliptic operators; weak Schatten norm estimates; Hankel operators; Connes metrics}}, language = {{eng}}, number = {{1}}, pages = {{363--406}}, publisher = {{European Mathematical Society Publishing House}}, series = {{Journal of Noncommutative Geometry}}, title = {{Commutator estimates on contact manifolds and applications}}, url = {{http://dx.doi.org/10.4171/JNCG/326}}, doi = {{10.4171/JNCG/326}}, volume = {{13}}, year = {{2019}}, }