JournalsjncgVol. 13, No. 1pp. 363–406

Commutator estimates on contact manifolds and applications

  • Heiko Gimperlein

    Heriot-Watt University, Edinburgh, UK and University of Paderborn, Germany
  • Magnus Goffeng

    Chalmers University of Technology and University of Gothenburg, Sweden
Commutator estimates on contact manifolds and applications cover

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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 DD is a first-order operator in the Heisenberg calculus and ff is Lipschitz in the Carnot–Carathéodory metric, then Œ[D,f][D, f] extends to an L2L^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.

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