| Título: | Harnack inequalities for subordinate Brownian motions |
| Autores: |
Mimica, Ante; University of Bielefeld Kim, Panki; Seoul National University |
| Fecha: | 2012-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: | Peer-reviewed Article |
| Tema: |
geometric stable process, Green function, Harnack inequality, Poisson kernel, harmonic function, potential, subordinator, subordinate Brownian motion Primary 60J45, Secondary 60G50, 60G51, 60J25, 60J27 |
| Descripción: | 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\[\phi(\lambda)=\log(1+(\lambda+m^{\alpha/2})^{2/\alpha}-m)\ (0<\alpha<2,\,m>0)\,.\] |
| Idioma: | Inglés |
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