Trace and Extension Theorems for Homogeneous Sobolev and Besov Spaces for Unbounded Uniform Domains in Metric Measure Spaces

In this paper we fix 1≤ p<∞ and consider (Ω,d,μ) to be an unbounded, locally compact, non-complete metric measure space equipped with a doubling measure μ supporting a p -Poincaré inequality such that Ω is a uniform domain in its completion Ω . We realize the trace of functions in the Dirichlet–Sobolev space D^1,p(Ω) on the boundary ∂Ω as functions in the homogeneous Besov space H-1pt B^α_p,p(∂Ω) for suitable α ; here, ∂Ω is equipped with a non-atomic Borel regular measure ν . We show that if ν satisfies a θ -codimensional condition with respect to μ for some 0<θ

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