For K-ary trees with a visual metric and weighted Newtonian spaces, the trace space is exactly a dyadic Besov-type space B^{θ,λ}_p, with borderline cases mapping to L^p or a distinct Besov-type space B^{0,λ}_α.
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Dyadic norm Besov-type spaces as trace spaces on regular trees
For K-ary trees with a visual metric and weighted Newtonian spaces, the trace space is exactly a dyadic Besov-type space B^{θ,λ}_p, with borderline cases mapping to L^p or a distinct Besov-type space B^{0,λ}_α.