In this talk, we discuss some potential theory of Dirichlet forms on
the half-space defined by the jump kernel
J(x,y)=|x−y|−d−αB(x,y)
and the killing potential κx−αd
, where α∈(0,2)
and B(x,y)
can blow up to
infinity at the boundary. The jump kernel and the killing potential
depend on several parameters. For all admissible values of the
parameters involved, we prove that the boundary Harnack principle
holds, and establish sharp two-sided estimates on the Green functions
of these processes.