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Bessel potentials, hitting distributions and Green functions


Authors: T. Byczkowski, J. Małecki and M. Ryznar
Journal: Trans. Amer. Math. Soc. 361 (2009), 4871-4900
MSC (2000): Primary 60J65; Secondary 60J60
DOI: https://doi.org/10.1090/S0002-9947-09-04657-1
Published electronically: April 10, 2009
MathSciNet review: 2506430
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Abstract: The purpose of the paper is to find explicit formulas for basic objects pertaining to the potential theory of the operator $ (I-\Delta)^{\alpha/2}$, which is based on Bessel potentials $ J_{\alpha}=(I-\Delta)^{-\alpha/2}$, $ 0<\alpha<2$. We compute the harmonic measure of the half-space and obtain a concise form for the corresponding Green function of the operator $ (I-\Delta)^{\alpha/2}$. As an application we provide sharp estimates for the Green function of the half-space for the relativistic process.


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Additional Information

T. Byczkowski
Affiliation: Institute of Mathematics and Computer Sciences, Wrocław University of Technology, ul. Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
Email: tomasz.byczkowski@pwr.wroc.pl

J. Małecki
Affiliation: Institute of Mathematics and Computer Sciences, Wrocław University of Technology, ul. Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
Email: jacek.malecki@pwr.wroc.pl

M. Ryznar
Affiliation: Institute of Mathematics and Computer Sciences, Wrocław University of Technology, ul. Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
Email: michal.ryznar@pwr.wroc.pl

DOI: https://doi.org/10.1090/S0002-9947-09-04657-1
Keywords: Bessel potential, Riesz kernel, relativistic process, stable process, Poisson kernel, Green function, half-space
Received by editor(s): February 6, 2007
Received by editor(s) in revised form: October 5, 2007
Published electronically: April 10, 2009
Additional Notes: This research was supported by DBN Grant 1P03A 020 28 and the second author was additionally supported by DBN Grant N N201 4100 33
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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