In this paper, we study a class of stochastic optimal control problem with
jumps under partial information. More precisely, the controlled systems are
described by a fully coupled nonlinear multi- dimensional forward-backward
stochastic differential equation driven by a Poisson random measure and an
independent multi-dimensional Brownian motion, and all admissible control
processes are required to be adapted to a given subfiltration of the filtration
generated by the underlying Poisson random measure and Brownian motion.
Backward stochastic partial differential equations of parabolic type with
variable coefficients are considered in the whole Euclidean space. Improved
existence and uniqueness results are given in the Sobolev space $H^n$
($=W^n_2$) under weaker assumptions than those used by X. Zhou [Journal of
Functional Analysis 103, 275--293 (1992)].