Analysis on manifolds and Lie groups
We are interested in the study of Laplacians and subLaplacians on noncompact Riemannian manifolds, as hyperbolic spaces and symmetric spaces, and on noncompact Lie. In particular, we introduce Sobolev and Besov spaces associated to such differential operators and study their properties. Such functional spaces play a role in the study of well-posedness results for nonlinear differential equations associated to the Laplacians and subLaplacians mentioned above.
Another interesting research field concerns the study of singular integrals and Fourier integral operators on Riemannian and subRiemannian manifolds and noncompact Lie groups. Riesz transforms, spectral multipliers of Laplacians and Fourier integral operators related with the wave equation are of particular interest. The classical techniques used in the euclidean setting do not apply in such contexts and one needs to introduce new functional spaces, like Hardy type spaces adapted to the geometry of the manifold and the group, to study boundedness properties of operators.