Commutator estimates on contact manifolds and applications
Heiko Gimperlein
Heriot-Watt University, Edinburgh, UK and University of Paderborn, GermanyMagnus Goffeng
Chalmers University of Technology and University of Gothenburg, Sweden
![Commutator estimates on contact manifolds and applications cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jncg-volume-13-issue-1.png&w=3840&q=90)
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 is a first-order operator in the Heisenberg calculus and is Lipschitz in the Carnot–Carathéodory metric, then extends to an -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.
Cite this article
Heiko Gimperlein, Magnus Goffeng, Commutator estimates on contact manifolds and applications. J. Noncommut. Geom. 13 (2019), no. 1, pp. 363–406
DOI 10.4171/JNCG/326