Bodies in space subject to solar ultraviolet flux will emit photoelectrons. At steady state the current of escaping photoelectrons is balanced by an influx of particles from the surrounding plasma. When the photoelectrons dominate the space charge close to the surface, it has previously been shown that two steady state potential distributions can exist, one in which the potential decreases from the surface value to zero monotonically and one in which it decreases to a negative minimum and then increases to zero. It has been suggested that the nonmonotonic distribution is the stable one. By assuming planar geometry and a Maxwellian distribution of the emitted photoelectrons the charging of isolated dust particles in the plasma sheath is calculated for both the monotonic and nonmonotonic potential distribution. By increasing photoemission from the surface from zero a transition from an ordinary Debye sheath above a nonilluminated surface to a photoelectron sheath is simulated. Dynamical properties of the dust particles such as oscillations, damping, stability, and trapping are investigated. After being injected into the sheath or electrostatically levitated, dust may be stably suspended above illuminated surfaces in space, even in the case of zero gravitation. However, the smallest particles may escape completely from the body. For all sheath types an unstable layer exists close to the surface where dust cannot collect. The theory is applied to bodies in the solar wind and to the spokes of Saturn.