Trace and extension theorems for functions of bounded variation

In this paper we show that every L1-integrable function on ∂Ω can be obtained as the trace of a function of bounded variation in Ω whenever Ω is a domain with regular boundary ∂Ω in a doubling metric measure space. In particular, when Ω supports a 1-Poincare inequality, the trace class of BV(Ω) is L1(∂Ω). We also construct a bounded linear extension from a Besov class of functions on ∂Ω to BV(Ω).