For every Bernstein function f, the f-subordinated heat semigroup satisfies Besov/Triebel-Lizorkin smoothing with rate [f^{-1}(1/t)]^{-d/2}.
Sato, L´ evy Processes and Infinitely Divisible Distributions, 2n d
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Bochner's Subordionation and Fractional Caloric Smoothing in Besov and Triebel--Lizorkin Spaces
For every Bernstein function f, the f-subordinated heat semigroup satisfies Besov/Triebel-Lizorkin smoothing with rate [f^{-1}(1/t)]^{-d/2}.