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.
A proof of Hörmander's theorem for sublaplacians on Carnot groups
BRANDOLINI, Luca
2015-01-01
Abstract
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.File allegato/i alla scheda:
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HormanderGruppiFInale.pdf
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