Occupation time densities for stable-like processes and other pure jump Markov processes

Pure jump Markov processes Xt on the line associated to the operators A[latin small letter f with hook](x)= [integral operator][[latin small letter f with hook](x+h)-[latin small letter f with hook](x)-[latin small letter f with hook]'(x)hl([-1,1])(h)][nu](x,dh) are considered. Sufficient conditions for Xt to have local times that serve as occupation time densities are given. In the case where [nu](x,dh)= h-(1+[alpha](x)), the stable-like case, these conditions reduce to: inf [alpha](x)>1 and [alpha](x) Dini continuous.