  In this paper, we are concerned with a stochastic optimal control problem of
mean-field type under partial observation, where the state equation is governed
by the controlled nonlinear mean-field stochastic differential equation,
moreover the observation noise is allowed to enter into the state equation and
the observation coefficients may depend not only on the control process and but
also on its probability distribution. Under standard assumptions on the
coefficients, by dual analysis and convex variation, we establish the maximum
principle for optimal control in a strong sense as well as a weak one,
respectively. As an application, a partially observed linear quadratic control
problem of mean-field type is studied detailed and the corresponding dual
characterization and state feedback presentation of the partially observed
optimal control are obtained by the stochastic maximum principles and the
classic technique of completing squares.
