Potential theory of Dirichlet forms with jump kernels blowing up at the boundary
Panki Kim, Renming Song, Zoran Vondraček · Journal of Functional Analysis · 2025
In this paper we study the potential theory of Dirichlet forms on the half-space R + d defined by the jump kernel J ( x , y ) = | x − y | − d − α B ( x , y ) and the killing potential κ x d − α , 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 and all d ≥ 1 , we prove that the boundary Harnack principle holds, and establish sharp two-sided estimates on the Green functions of these processes.