Optimal local Hölder index for density states of superprocesses with $(1+\beta )$-branching mechanism

Klaus Fleischmann, Leonid Mytnik, Vitali Wachtel

For $0<\alpha \le 2$, a super-$\alpha$-stable motion $X$ in ${\mathsf{R}}^d$ with branching of index $1+\beta \in (1,2)$ is considered. Fix arbitrary $t>0$. If $d<\alpha /\beta$, a dichotomy for the density fu…