  We study nonlocal elliptic and parabolic equations on $C^{1,\tau}$ open sets
in weighted Sobolev spaces, where $\tau\in (0,1)$. The operators we consider
are infinitesimal generators of symmetric stable L\'evy processes, whose L\'evy
measures are allowed to be very singular. Additionally, for parabolic
equations, the measures are assumed to be merely measurable in the time
variable.
