Seminario di analisi matematica
ore
16:30
presso Seminario II
In this talk we present some recent results obtained in collaboration
with B. Franchi and P. Pansu about Poincaré and Sobolev inequalities in
Heisenberg groups (some results are new also for Euclidean spaces). For
$L^p$, $p>1$, the estimates are consequence of singular integral
estimates. I would like to concentrate the seminar, in particular, to
the limiting case $L^1$, where the exterior Rumin-differential of a
differential form is measured in $L^1$ norm. Unlike for $L^p$, $p>1$,
the estimates are doomed to fail in top degree. In the limiting case,
the singular integral estimates are replaced with inequalities which go
back to Bourgain-Brezis and Lanzani-Stein in Euclidean spaces, and to
Chanillo-Van Schaftingen and Baldi-Franchi-Pansu in Heisenberg groups.