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arXiv · 1312.7677

Commutator estimates on contact manifolds and applications

Heiko Gimperlein·Magnus Goffeng
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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 Calderon commutator estimate: If $D$ is a first-order operator in the Heisenberg calculus and $f$ is Lipschitz in the Carnot-Caratheodory metric, then $[D,f]$ extends to an $L^2$-bounded operator. Using interpolation, it implies sharp weak--Schatten class properties for the commutator between zeroth order operators and H\"older 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.

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Heiko Gimperlein, Magnus Goffeng. 2013-12-30. Commutator estimates on contact manifolds and applications. https://doi.org/10.4171/jncg%2F326

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