Bochner's subordination and fractional caloric smoothing in Besov and Triebel–Lizorkin spaces

We use Bochner's subordination technique to obtain caloric smoothing estimates in Besov‐ and Triebel–Lizorkin spaces. Our new estimates extend known smoothing results for the Gauß–Weierstraß, Cauchy–Poisson and higher‐order generalized Gauß–Weierstraß semigroups. Extensions to other function spaces (homogeneous, hybrid) and more general semigroups are sketched.