Sharp two-sided Green function estimates for Dirichlet forms degenerate at the boundary

The goal of this paper is to establish Green function estimates for a class purely discontinuous symmetric Markov processes with jump kernels degenerate at the boundary and critical killing potentials. kernel potential depend on several parameters. We sharp two-sided functions these all admissible values parameters involved. Depending regions where belong, are different. In fact, have three different forms. As applications, we prove that Harnack principle holds in certain region fails some other Together main results our previous \[Potential Anal., online, 2021], completely determine holds.