Interpolation properties of Besov spaces defined on metric spaces

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Measure Density and Extension of Besov and Triebel–Lizorkin Functions (2014, methodology): “In addition to the definition based on pointwise inequalities, we will sometimes use a generalization to the metric setting of the classical definition of the Besov spaces via the L-modulus of smoothness; this general version was introduced in [9].”
Characterizations of Besov and Triebel–Lizorkin spaces on metric measure spaces (2011, background): “For the theory of Besov spaces on Rn see, for example, [25, 22, 26], and, on metric measure spaces, see [9, 21, 7].”
Besov class via heat semigroup on Dirichlet spaces II: BV functions and Gaussian heat kernel estimates (2018, methodology): “We begin by comparing the heat semigroupbased Besov class Bp,α/2(X) introduced in [2] to a more classical Besov class Bα p,∞(X) that was defined in [38] from the intrinsic metric dE rather than the heat semigroup Pt.”
Pointwise Characterizations of Besov and Triebel-Lizorkin Spaces and Quasiconformal Mappings (2010, methodology): “For the characterizations of Besov and Triebel-Lizorkin spaces via differences on metric measure spaces, see [23, 10].”