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On Estimates of Transition Density for Subordinate Brownian Motions with Gaussian Components in C1,1-open Sets

  • Joohak Bae
  • Panki Kim
Article
  • 3 Downloads

Abstract

We consider a subordinate Brownian motion X with Gaussian components when the scaling order of purely discontinuous part is between 0 and 2 including 2. In this paper we establish sharp two-sided bounds for transition density of X in \({\mathbb {R}}^{d}\) and C1,1-open sets. As a corollary, we obtain a sharp Green function estimates.

Keywords

Dirichlet heat kernel Transition density Laplace exponent Lévy measure Subordinator Subordinate Brownian motion 

Mathematics Subject Classification (2010)

Primary 60J35, 60J50, 60J75 Secondary 47G20 

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Notes

Acknowledgments

We are grateful to the referee for suggesting a short proof of Lemma 2.4.

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Mathematical SciencesSeoul National UniversitySeoulRepublic of Korea
  2. 2.Department of Mathematical Sciences and Research Institute of MathematicsSeoul National UniversitySeoulRepublic of Korea

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