Title: Some Functional Analysis and A Harnack Inequality for the Fractional Laplacian in Homogeneous groups.

Abstract:  This talk will discuss some basic functional analysis in the setting of homogeneous group.  In particular, we will be concerned with the spaces of distributions with finite fractional norm.  I will present Sobolev embedding theorems for such spaces as well as a discussion of regularity of solutions to the fractional Laplacian which live in these spaces, including a Harnack inequality.   The novelty of these results is that they are obtained in a setting with no Hormnader condition, so that many of the familiar tools of geometry are not available - as such this talk will likely have more the flavor of analysis rather than geometry.  Yum?