Abstract
In this paper, we derive explicit sharp two-sided estimates for the Dirichlet heat kernels, in C1,1 open sets D in ℝd, of a large class of subordinate Brownian motions with Gaussian components. When D is bounded, our sharp two-sided Dirichlet heat kernel estimates hold for all t > 0. Integrating the heat kernel estimates with respect to the time variable t, we obtain sharp two-sided estimates for the Green functions, in bounded C1,1 open sets, of such subordinate Brownian motions with Gaussian components.
Funding source: NSF
Award Identifier / Grant number: DMS-1206276
Funding source: NNSFC
Award Identifier / Grant number: 11128101
Funding source: National Research Foundation of Korea (NRF), Korea government (MSIP)
Award Identifier / Grant number: 2009-0083521
Funding source: Simons Foundation
Award Identifier / Grant number: 208236
We thank the referee for helpful comments.
© 2016 by De Gruyter
