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Boundedness for pseudo-differential calculus on nilpotent Lie groups. (English) Zbl 1322.47046
Kielanowski, Piotr (ed.) et al., Geometric methods in physics. XXXI workshop, Białowieża, Poland, June 24–30, 2012. Selected papers based on the presentations at the workshop. Basel: Birkhäuser/Springer (ISBN 978-3-0348-0644-2/hbk; 978-3-0348-0645-9/ebook). Trends in Mathematics, 87-97 (2013).
The aim of this paper is to survey some boundedness results for the Weyl-Pedersen pseudo-differential calculus on nilpotent Lie groups in the case of flat orbits and to give applications to some three-step nilpotent groups that have non-flat generic orbits. These results generalize the Calderón-Vaillancourt theorem.
For the entire collection see [Zbl 1271.00030].

MSC:
47G30 Pseudodifferential operators
35S05 Pseudodifferential operators as generalizations of partial differential operators
22E25 Nilpotent and solvable Lie groups
47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
35R03 PDEs on Heisenberg groups, Lie groups, Carnot groups, etc.
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