  We study the problem of existence and uniqueness of solutions of backward
stochastic differential equations with two reflecting irregular barriers, $L^p$
data and generators satisfying weak integrability conditions. We deal with
equations on general filtered probability spaces. In case the generator does
not depend on the $z$ variable, we first consider the case $p=1$ and we only
assume that the underlying filtration satisfies the usual conditions of
right-continuity and completeness. Additional integrability properties of
solutions are established if $p\in(1,2]$ and the filtration is quasi-left
continuous. In case the generator depends on $z$, we assume that $p=2$, the
filtration satisfies the usual conditions and additionally that it is
separable. Our results apply for instance to Markov-type reflected backward
equations driven by general Hunt processes.
