In this talk, we discuss transition densities of pure jump symmetric Markov processes in $\mathbb{R}^d$, whose jumping kernels are comparable to radially symmetric functions with general mixed polynomial growths. Under some mild assumptions on their scale functions, we establish sharp two-sided estimates of transition densities (heat kernel estimates) for such processes.

This is a joint work with Joohak Bae, Jaehoon Kang and Jaehun Lee.