Bochner's Subordionation and Fractional Caloric Smoothing in Besov and Triebel--Lizorkin Spaces

英文摘要：

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.