Abstract
Let {Xt}t≥0 be the α-stable-like or relativislic α-stable-like process on ℝd generated by a certain symmetric jump-type regular Dirichlet form (ε,F). It is known in [5,7] that the transition probability density p(t,x,y) of {Xt}t≥0 admits the two-sided estimates. Let μ be a positive smooth Radon measure in a certain class and consider the perturbed form εμ(u,u) = ε(u,u) - (u,u)μ. Denote by pμ(t,x,y) the fundamental solution associated with εμ. In this paper, we establish a necessary and sufficient condition on μ for pμ(t. x, y) having the same two-sided estimates as p(t, x, y) up to positive constants.
Original language | English |
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Pages (from-to) | 523-537 |
Number of pages | 15 |
Journal | Tohoku Mathematical Journal |
Volume | 66 |
DOIs | |
Publication status | Published - 2014 Dec |
Externally published | Yes |
Keywords
- Dirichlet forms
- Heat kernel
- Markov processes
- Perturbation
ASJC Scopus subject areas
- Mathematics(all)