Special Session 110: Stochastic Dynamics

$L_p$-estimates for nonlocal equations with general L\`evy measures
Junhee Ryu
KIAS
Korea
Co-Author(s):    Hongjie Dong
Abstract:
In this talk, we consider time-dependent nonlocal operators associated with general L\`evy measures of order $\sigma \in(0,2)$. We allow the class of L\`evy measures to be very singular and impose no regularity assumptions in the time variable. Continuity of the operators and the unique strong solvability of the corresponding nonlocal parabolic equations in $L_p$ spaces are established. We also demonstrate that, depending on the ranges of $\sigma$ and $d$, the operator can or cannot be treated in weighted mixed-norm spaces.