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 Holder 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.

Ämnesord

NATURVETENSKAP  -- Matematik -- Algebra och logik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Algebra and Logic (hsv//eng)

NATURVETENSKAP  -- Matematik -- Geometri (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Geometry (hsv//eng)

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Nyckelord

Heisenberg calculus

weak Schatten norm estimates

hypoelliptic operators

Hankel operators

Commutator estimates

Connes metrics

Commutator estimates

Connes metrics

Hankel operators

Heisenberg calculus

Hypoelliptic operators

Weak Schatten norm estimates

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art (ämneskategori)

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