Two-sided heat kernel estimates for censored stable-like processes

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The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion (2017, methodology): “The Green function G(x, y) satisfies condition (K4) with γ = s− 12 , as proven by Chen, Kim and Song [86].”
Dirichlet heat kernel estimates for Δα/2 + Δβ/2 (2010, methodology): “Although we follow the general strategy developed in [6], there are several new difficulties to overcome in obtaining two-sided Dirichlet heat kernel estimates for Xa.”
Regularity results for nonlocal parabolic equations (2013, background): “2) is taken over Ω instead of the full space, are proved in [20].”
Heat kernel estimates and Harnack inequalities for some Dirichlet forms with non-local part (2009, background): “In Chapter 7 of [3], it is shown that for any regular Dirichlet form, there exists a Hunt process whose Dirichlet form is the given regular one.”
Dirichlet heat kernel estimates for rotationally symmetric Lévy processes (2013, background): “Sharp two-sided Dirichlet heat kernel estimates in C1,1 open sets are subsequently established in [12, 14, 13, 15] for censored stable processes, relativistic stable processes, mixed stable processes, and mixed Brownian motion and stable processes, respectively.”
A Priori Estimates for Fractional Nonlinear Degenerate Diffusion Equations on Bounded Domains (2013, background): “2 of [18], as a consequence of sharp heat kernel estimates.”