General gauge and conditional gauge theorems

By Zhen-Qing Chen, Renming Song. 2002

76 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/a8adc6030af17a1788c719801aa9f0c1a2ff551c

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Citations in the corpus

Potential theory of truncated stable processes (2006, methodology): “Since qD is bounded, one can use the 3G-type estimates for symmetric stable processes in [29] to check that qD belongs to the class S∞(X) there, thus it follows from [15] or [16] that GD(x, y) is continuous and there exists a positive constant C such that GD(x, y) ≤ GD(x, y) ≤ CGD(x, y), ∀x, y ∈ D.”
Estimates of the Green Function for the Fractional Laplacian Perturbed by Gradient (2010, background): “In particular Schrödinger perturbations of ∆ were studied by Chen and Song ([19], [21]), Bogdan and Byczkowski ([7], [8]), Bogdan, Hansen and Jakubowski ([11]) and Bogdan, Burdzy and Chen ([6]).”
Two-sided estimates on the density of Brownian motion with singular drift (2006, unknown): “For the proof of the last inequality, one can see the proof of Proposition 4.2 in [ 7 ].”
Drift transforms and Green function estimates for discontinuous processes (2003, methodology): “We first recall the following definitions from Chen [6], which extend those in Chen and Song [9] [10].”
Differentiability of spectral functions for symmetric $\alpha$-stable processes (2007, unknown): “[11]).”
Intrinsic Ultracontractivity for Schrödinger Operators Based on Fractional Laplacians (2009, background): “[19] E. B. Davies, B. Simon, Ultracontractivity and heat kernels for Schrödingers operators and Dirichlet Laplacians, J. Funct.”
Conditional gauge theorem for non-local Feynman-Kac transforms (2003, methodology): “For each fixed z ∈ E, set Ez := {x ∈ E : 0 G(x, z) ∞} We are also going use (N̂(x, dy), Ĥt ), where N̂(x, dy) is a Borel kernel on (E,B(E∂)) and Ĥt is a positive continuous additive functional of X̂ with bounded 1-potential, to denote a Lévy system of X̂.”