@article{df57aa611aa44efcab1205096c5bc806,
title = "Powers of Brownian Green Potentials",
abstract = "In this article we study stability properties of gO, the standard Green kernel for O an open regular set in ℝd. In d ≥ 3 we show that gOβ is again a Green kernel of a Markov Feller process, for any power β ∈ [1,d/(d − 2)). In dimension d = 2, we show the same result for gOβ, for any β ≥ 1 and for kernels exp(αgO),exp(αgO)−1, for α ∈ (0,2π), when O is an open Greenian regular set whose complement contains a ball.",
keywords = "Brownian motion, Green potentials, Markov processes",
author = "Claude Dellacherie and Mauricio Duarte and Servet Mart{\'i}nez and Mart{\'i}n, {Jaime San} and Pierre Vandaele",
note = "Funding Information: The authors are thankful to Martin Barlow, who pointed out the results in [] for the existence of density in the context of symmetric Markov Processes. We are also indebted to Krzysztof Burdzy for helpful discussions on the 2d case. Finally, we thank an anonymous referee for his/her careful reading and suggestions, which allowed us to improve the presentation of this article. S.M., J.S.M. and P.V. were supported by CONICYT BASAL AFB170001. M.D. was supported in part by Milenio NC120062. Publisher Copyright: {\textcopyright} 2021, Springer Nature B.V. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",
year = "2021",
month = jan,
day = "23",
doi = "10.1007/s11118-020-09883-z",
language = "English",
journal = "Potential Analysis",
issn = "0926-2601",
publisher = "Springer Netherlands",
}