The distance from f to a subspace V of the inhomogeneous Lipschitz space Λ_s is equivalent to a critical index measuring where the fractional heat semigroup derivative ∂^r_t T_{α,t} f exceeds ε t^{s-rα}.
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Fractional Heat Semigroup Characterization of Distances from Functions in Lipschitz Spaces to Their Subspaces
The distance from f to a subspace V of the inhomogeneous Lipschitz space Λ_s is equivalent to a critical index measuring where the fractional heat semigroup derivative ∂^r_t T_{α,t} f exceeds ε t^{s-rα}.