Following Bernicot (2012) [7], we introduce a notion of paraproducts associated to a semigroup. We do not use Fourier transform arguments and the background manifold is doubling, endowed with a sub-Laplacian structure. Our main result is a paralinearization theorem in a non-Euclidean framework, with an application to the propagation of regularity for some nonlinear PDEs.
@article{AIHPC_2013__30_5_935_0, author = {Bernicot, Fr\'ed\'eric and Sire, Yannick}, title = {Propagation of low regularity for solutions of nonlinear PDEs on a Riemannian manifold with a sub-Laplacian structure}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {30}, year = {2013}, pages = {935-958}, doi = {10.1016/j.anihpc.2012.12.005}, zbl = {06295447}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_2013__30_5_935_0} }
Bernicot, Frédéric; Sire, Yannick. Propagation of low regularity for solutions of nonlinear PDEs on a Riemannian manifold with a sub-Laplacian structure. Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) pp. 935-958. doi : 10.1016/j.anihpc.2012.12.005. http://gdmltest.u-ga.fr/item/AIHPC_2013__30_5_935_0/
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