Trace and Extension Theorems for Besov Functions in Doubling Metric Measure Spaces

In the setting of a non-complete doubling metric measure space (Ω, d, μ), we construct various bounded linear trace and extension operators for homogeneous and inhomogeneous Besov spaces B^α₏, ₐ. Equipping the boundary Ω: =ΩΩ with a measure which is codimension θ Ahlfors regular with respect to μ, these operators take the form \ T: B^α₏, ₐ (Ω) B^α-θ/p₏, ₐ (Ω), E: B^α₏, ₐ (Ω) B^α+θ/p₏, ₐ (Ω). \ The trace operators are first constructed under the additional assumption that Ω is a uniform domain in its completion. We then use such results along with the technique of hyperbolic filling to remove this assumption in the case that Ω is bounded. This extends to the doubling setting some earlier results of Marcos and Saksman-Soto proven under the assumption that the ambient measure is Ahlfors regular.