Daehong Kim, Panki Kim, Kazuhiro Kuwae
Published 2022-04-04Version 1
In this paper, when a given symmetric Markov process X satisfies the stability of global heat kernel two-sided (upper) estimates by Markov perturbations, we give a necessary and sufficient condition on the stability of global two-sided (upper) estimates for fundamental solution of Feynman-Kac semigroup of X. As a corollary, under the same assumptions, a weak type global two-sided (upper) estimates holds for the fundamental solution of Feynman-Kac semigroup with (extended) Kato class conditions for measures. This generalizes all known results on the stability of global integral kernel estimates by symmetric Feynman-Kac perturbations with Kato class conditions in the framework of symmetric Markov processes.
On the Estimates of the Density of Feynman-Kac Semigroups of $α$-Stable-like Processes
Explosion by Killing and Maximum Principle in Symmetric Markov Processes
Hölder continuity and bounds for fundamental solutions to non-divergence form parabolic equations
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