Time: 2017-12-13 15:30-16:30
The question of when a Sobolev space is an algebra has a long history.
In this talk, we first review the classical problem and its variation in R^n (due
to Strichartz) and on a nilpotent Lie group. We also discuss the possible definitions
of Sobolev spaces in more general settings, such as a manifold or a Lie group,
and in terms of a sublaplacian. We then show how to solve the question of when a
Sobolev space is an algebra on a general Lie group, where the Sobolev space is
defined in terms of a sublaplacian. Then we discuss a number of open problem
that arose from this work, which is in collaboration with M. Vallarino.