In this talk, we discuss transition densities of pure jump symmetric Markov processes in 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.

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