Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Commutator estimates on contact manifolds and applications   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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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: cs
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The categories of this paper are: chem-ph