Part 2

A.A. 1998/99

**Lecturer: Francesco Serra Cassano**

**Programme**

Covering theorms and maximal function on metric spaces.

Lipischitz maps between metric spaces.

Classical Sobolev spaces and type Sobolev-Poincare' inequalities.

Sobolev spaces on metric spaces. Sobolev spaces equipped with Carnot-Caratheodory
(C-C) metrics

A first approach to a Gemotric Measure Theory in a space eqipped with
a C-C metric: isoperimetric inequality, coarea formula, reduced boundary.