  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.
