Weighted Poincaré inequality and heat kernel estimates for finite range jump processes

By Zhen-Qing Chen, Panki Kim, Takashi Kumagai. 2008

107 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/09b59ac0efc64b347237d3b69508816f124f0895

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Conservation property of symmetric jump processes (2011, background): “It is proved in [2,5] (see also [4]) that the processes associated to k on R in Examples 4.”
Dirichlet heat kernel estimates for rotationally symmetric Lévy processes (2013, background): “When X is a pure jump symmetric process on Rd, sharp estimates on p(t, x, y) have been studied in [8, 9, 10, 17, 18] recently, which can be viewed as the counterpart of Aronson’s estimates for non-local operators.”
Transition Density Estimates for a Class of Lévy and Lévy-Type Processes (2009, background): “Pure jump processes whose jump kernel is comparable to the one of truncated stable-like process are considered by Chen, Kim and Kumagai [10].”
Regularity results for nonlocal parabolic equations (2013, background): “A more involved proof for a smaller class of weights and not being robust for α→ 2− can be found in [16].”
Estimates of Tempered Stable Densities (2008, methodology): “The asymptotics of the densities of the truncated stable-like processes have been investigated by Chen, Kim, and Kumagai [ 3 ].”
On Harnack Inequality and Hölder Regularity for Isotropic Unimodal Lévy Processes (2013, result): “Note that similar condition as (A1) appeared in [4] and [1] and exactly the same in [5] and [6].”
On heat kernel estimates and parabolic Harnack inequality for jump processes on metric measure spaces (2009, background): “Running title: Notes on Heat Kernel Estimates and Parabolic Harnack Inequality”
On weighted Poincar\'e inequalities (2012, background): “Let F : L(X)× ((1) 2 , 1] → [0,∞] be a functional satisfying F (u+ a, r) = F (u, r), a ∈ R, (2) ˆ”
Heat kernel estimates for the Dirichlet fractional Laplacian (2009, background): “Although two-sided heat kernel estimates for jump processes in R have been studied recently by several authors (see [8, 9, 5] and the references therein), as far as we know, this is the first time that sharp two-sided estimates on the Dirichlet heat kernels for jump processes in open sets are establ”
On weighted Poincaré inequalities (2012, background): “Because of (2), by subtracting a constant from u, we may and do assume that uφB1 = 0, which means that (6) 0 = ˆ B1 u(x)φ(x) dx = ˆ 1”
Symmetric jump processes and their heat kernel estimates (2009, methodology): “The heat kernel estimates obtained in [14] shows finite range stable-like processes behave like discontinuous stablelike processes in small scale and behave like Brownian motion in large scale.”