Fractional heat semigroup kernels on metric measure spaces satisfy Euclidean-style decay, yielding Strichartz regularity and capacity-based trace criteria for fractional dissipative Cauchy problems.
Cheeger, Differentiability of Lipschitz functions on metric measure spaces, GAF A 9:3 (1999), 428-517
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Fractional heat semigroups on metric measure spaces with finite densities and applications to fractional dissipative equations
Fractional heat semigroup kernels on metric measure spaces satisfy Euclidean-style decay, yielding Strichartz regularity and capacity-based trace criteria for fractional dissipative Cauchy problems.