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Harnack inequalities for subordinate Brownian motions

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Harnack inequalities for subordinate Brownian motions
2.	Creator	Author's name, affiliation, country	Ante Mimica; University of Bielefeld; Germany
2.	Creator	Author's name, affiliation, country	Panki Kim; Seoul National University; Korea, Republic Of
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	geometric stable process, Green function, Harnack inequality, Poisson kernel, harmonic function, potential, subordinator, subordinate Brownian motion
3.	Subject	Subject classification	Primary 60J45, Secondary 60G50, 60G51, 60J25, 60J27
4.	Description	Abstract	In this paper, we consider subordinate Brownian motion  $X$ in $\mathbb{R}^d$, $d \ge 1$,  where the Laplace exponent $\phi$ of the corresponding subordinator satisfies some mild conditions. The scale invariant Harnack inequality  is proved for $X$.   We first give new forms of asymptotical properties of the Lévy and potential density of the subordinator near zero. Using these results we find asymptotics of the Lévy density and potential density of $X$ near the origin, which is essential to our approach. The examples which are covered byour results include geometric stable processes and relativistic geometric stable processes, i.e. the cases when the subordinator has the Laplace exponent\[\phi(\lambda)=\log(1+\lambda^{\alpha/2})\  (0<\alpha\leq 2)\]and\[\phi(\lambda)=\log(1+(\lambda+m^{\alpha/2})^{2/\alpha}-m)\ (0<\alpha<2,\,m>0)\,.\]
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2012-05-27
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/1930
10.	Identifier	Digital Object Identifier	10.1214/EJP.v17-1930
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 17
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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