# The equivalence between the pointwise Hardy inequality and the uniform capacity density condition

## Riikka Korte

### (University of Helsinki)

Date: Jan 13, 2011, time: 16:50

Place: Centro De Giorgi, Scuola Normale Superiore

Abstract. I will discuss the relationship between Hardy's inequality, a pointwise Hardy inequality, a uniform capacity density condition and a boundary Poincaré inequality in doubling metric spaces supporting a Poincaré inequality. All of these conditions can be used to describe the size of the boundary of a set. In particular, I will concentrate in explaining the main ideas behind the proof of the equivalence of the three conditions. The talk is based on joint work with Juha Lehrbäck and Heli Tuominen.