  We present Submillimeter Array observations of the z=3.91 gravitationally
lensed broad absorption line quasar APM08279+5255 which spatially resolve the
1.0mm (0.2mm rest-frame) dust continuum emission. At 0.4" resolution, the
emission is separated into two components, a stronger, extended one to the
northeast (46+/-5mJy) and a weaker, compact one to the southwest (15+/-2mJy).
We have carried out simulations of the gravitational lensing effect responsible
for the two submm components in order to constrain the intrinsic size of the
submm continuum emission. Using an elliptical lens potential, the best fit
lensing model yields an intrinsic (projected) diameter of ~80pc, which is not
as compact as the optical/near-infrared (NIR) emission and agrees with previous
size estimates of the gas and dust emission in APM08279+5255. Based on our
estimate, we favor a scenario in which the 0.2mm (rest-frame) emission
originates from a warm dust component (T_d=150-220K) that is mainly heated by
the AGN rather than by a starburst (SB). The flux is boosted by a factor of ~90
in our model, consistent with recent estimates for APM08279+5255.
