Seminario: Operatori ipoellittici e teoremi ottimali sui moltiplicatori

Giovedì 17 Ottobre 2013, ore 12:15 - Aula Richard - Alessio Martini


Giovedì 17 Ottobre 2013 alle ore 12:15 in aula Richard Alessio Martini (Christian-Albrechts-Universität zu Kiel) terrà un seminario dal titolo "Operatori ipoellittici e teoremi ottimali sui moltiplicatori".

Let L be the Laplacian on R^n. The investigation of necessary and sufficient conditions for an operator of the form F(L) to be bounded on L^p in terms of "smoothness properties" of the spectral multiplier F is a classical research area of harmonic analysis, with long-standing open problems (e.g., the Bochner-Riesz conjecture) and connections with the regularity theory of PDEs.
In settings other than the Euclidean, particularly in the presence of a sub-Riemannian geometric structure, the natural substitute L for the Laplacian need not be an elliptic operator, and it may be just hypoelliptic. In this context, even the simplest questions related to the L^p-boundedness of operators of the form F(L) are far from being completely understood.
I will present some recent results, obtained in joint work with Detlef Müller (Kiel), dealing with the case of sublaplacians on 2-step stratified (Carnot) groups, and with Grushin operators.