Revista Matemática Iberoamericana


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Volume 30, Issue 4, 2014, pp. 1439–1478
DOI: 10.4171/RMI/821

Published online: 2014-12-15

Semiclassical hypoelliptic estimates with a loss of many derivatives

Alberto Parmeggiani[1] and Karel Pravda-Starov[2]

(1) Università di Bologna, Italy
(2) Université de Rennes I, France

We study the pseudospectral properties of general pseudodifferential operators around a doubly characteristic point and provide necessary and sufficient conditions for semiclassical hypoelliptic a priori estimates with a loss of many derivatives.

Keywords: Resolvent estimates, doubly characteristic pseudodifferential operators, hypoellipticity with a loss of many derivatives, Grushin-reduction method

Parmeggiani Alberto, Pravda-Starov Karel: Semiclassical hypoelliptic estimates with a loss of many derivatives. Rev. Mat. Iberoam. 30 (2014), 1439-1478. doi: 10.4171/RMI/821