Bochner's Subordionation 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 Gau{\ss}–Weierstra{\ss}, Cauchy–Poisson and higher-order generalized Gau{\ss}–Weierstra{\ss} semigroups. Extensions to other function spaces (homogeneous, hybrid) and more general semigroups are sketched.