86 citations · 347 across the 33 of their papers we have counts for
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Estimates of Dirichlet heat kernel for symmetric Markov processes
Tomasz Grzywny, Kyung-Youn Kim, Panki Kim
We consider a large class of symmetric pure jump Markov processes dominated by isotropic unimodal Lévy processes with weak scaling conditions. First, we establish sharp two-sided h…
Green function for gradient perturbation of unimodal Lévy processes
Tomasz Grzywny, Tomasz Jakubowski, Grzegorz Żurek
We prove that the Green function of a generator of isotropic unimodal Lévy processes with the weak lower scaling order bigger than one and the Green function of its gradient pertur…
Asymptotic behavior of densities of unimodal convolution semigroups
Wojciech Cygan, Tomasz Grzywny, Bartosz Trojan
We prove the asymptotic formulas for the transition densities of isotropic unimodal convolution semigroups of probability measures on under the assumption that its L…
Kato classes for Lévy processes
Tomasz Grzywny, Karol Szczypkowski
We prove that the definitions of the Kato class by the semigroup and by the resolvent of the Lévy process on coincide if and only if 0 is not regular for {0}. If 0 i…
Hitting times of points and intervals for symmetric Lévy processes
Tomasz Grzywny, Michał Ryznar
For one-dimensional symmetric Lévy processes, which hit every point with positive probability, we give sharp bounds for the tail function of the first hitting time of B which is ei…