… We give sharp bounds for the isotropic unimodal probability convolution semigroups
when their Lévy–Khintchine exponent has Matuszewska indices strictly between 0 and 2. …
Put differently, we study the vaguely continuous spherically isotropic unimodal convolution
semigroups ( p t , t ⩾ 0 ) of probability measures on R d with purely nonlocal generators. (In
this work we never use probabilistic techniques beyond the level of one-dimensional
distributions of X.) … Namely, in Theorem 26 we show that for unimodal Lévy processes …