General gauge and conditional gauge theorems

Abstract

General gauge and conditional gauge theorems are established for a large class of (not necessarily symmetric) strong Markov processes, including Brownian motions with singular drifts and symmetric stable processes. Furthermore, new classes of functions are introduced under which the general gauge and conditional gauge theorems hold. These classes are larger than the classical Kato class when the process is Brownian motion in a bounded $C^{1,1}$ domain.