Global heat kernel estimate for relativistic stable processes in exterior open sets

Zhen Qing Chen, Panki Kim, Renming Song

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, sharp two-sided estimates for the transition densities of relativistic α-stable processes with mass m∈(0, 1] in C 1,1 exterior open sets are established for all time t>0. These transition densities are also the Dirichlet heat kernels of m-(m 2/α-δ) α/2 with m∈(0, 1] in C 1,1 exterior open sets. The estimates are uniform in m in the sense that the constants are independent of m∈(0, 1]. As a corollary of our main result, we establish sharp two-sided Green function estimates for relativistic α-stable processes with mass m∈(0, 1] in C 1,1 exterior open sets.

Original languageEnglish (US)
Pages (from-to)448-475
Number of pages28
JournalJournal of Functional Analysis
Volume263
Issue number2
DOIs
StatePublished - Jul 15 2012

Keywords

  • Exit time
  • Green function
  • Heat kernel
  • Lévy system
  • Parabolic Harnack inequality
  • Relativistic stable process
  • Symmetric α-stable process
  • Transition density

ASJC Scopus subject areas

  • Analysis

Fingerprint Dive into the research topics of 'Global heat kernel estimate for relativistic stable processes in exterior open sets'. Together they form a unique fingerprint.

Cite this