On Regularity for Beurling–Deny Type Dirichlet Forms

Characteristic examples of Beurling–Deny type Dirichlet forms are considered. The forms are identified with bilinear forms of integro-differential operators that arise as generators of jump-diffusion processes. The aim of this article is to prove Harnack inequalities for these operators and consequently Hölder regularity of weak H¹-solutions. Moser's iteration technique is used.