Pierre Portal

Australian National University

Beyond Calderon-Zygmund theory in Bochner spaces

In the past few years many results on singular integral operators have been extended from the scalar-valued setting to the case of Bochner spaces Lp(Rn;X) where X is a UMD Banach space. The interest of such a generalization lies in its applications to nonlinear PDE and the insight it provides on some geometric properties of Banach spaces and on a probabilistic approach to harmonic analytic questions. This talk will present some of these results and, in particular, recent developments on operators which fall beyond the scope of Calderón-Zygmund theory.