A proof of Hörmander’s theorem for sublaplacians on Carnot groups

We give a self-contained analytical proof of Hörmander’s hypoellipticity theorem in the case of left invariant sub-laplacians of Carnot groups. The proof does not rely on pseudodifferential calculus and provides intermediate regularity estimates expressed in terms of Sobolev spaces induced by right...

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Bibliographic Details
Published in:Nonlinear analysis 2015-10, Vol.126, p.170-200
Main Authors: Bramanti, Marco, Brandolini, Luca
Format: Article
Language:English
Subjects:
Calculus
Fields (mathematics)
Hypoelliptic operators
Hörmander’s hypoellipticity theorem
Invariants
Mathematical analysis
Proving
Regularity
Sobolev space
Theorems
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Summary:We give a self-contained analytical proof of Hörmander’s hypoellipticity theorem in the case of left invariant sub-laplacians of Carnot groups. The proof does not rely on pseudodifferential calculus and provides intermediate regularity estimates expressed in terms of Sobolev spaces induced by right invariant vector fields.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2015.02.021