CRM: Centro De Giorgi
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Dispersive and subelliptic PDEs

Two-parameter harmonic analysis on the Heisenberg group

speaker: Fulvio Ricci (Scuola Normale Superiore)

abstract: Besides the widely studied sub-Riemannian metric, the Heisenberg group also possesses a natural left-invariant Riemannian distance, in which the basic vector fields X, Y, T form an orthonormal frame at each point. In the study of the de-bar-Neumann problem in several complex variables or of the Riemannian Hodge Laplacian, it has been observed (Phong-Stein in 1982, Müller-Peloso-Ricci and Nagel-Stein more recently) that both metrics may appear simultaneously, which requires an understanding of compositions of operators of Riemannian and sub-Riemannian nature. One example is the composition of the two (one-parameter) Hardy-Littlewood maximal operators, where each involves averages over balls in the respective metric.

Wed 12 Feb, 11:30 - 12:20, Aula Dini


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