L^p estimates for Feynman-Kac propagators with time-dependent reference measures

We introduce a class of time-inhomogeneous transition operators of Feynman-Kac type that can be considered as a generalization of symmetric Markov semigroups to the case of a time-dependent reference measure. Applying weighted Poincar\'e and logarithmic Sobolev inequalities, we derive L^p-L^p and L^p-L^q estimates for the transition operators. Since the operators are not Markovian, the estimates depend crucially on the value of p. Our studies are motivated by applications to sequential Markov Chain Monte Carlo methods.