We calculate some extremal and non-extremal four-point functions on the
sphere of certain chiral primary operators for strings on AdS_3 x S^3 x T^4.
The computation is done for small values of the spacetime cross-ratio where
global SL(2) and SU(2) descendants may be neglected in the intermediate
channel. Ignoring also current algebra descendants, we find that in the
non-extremal case the integrated worldsheet correlators factorize into
spacetime three-point functions, which is non-trivial due to the integration
over the moduli space. We then restrict to the extremal case and compare our
results with the four-point correlators recently computed in the dual boundary
theory. We also discuss a particular non-extremal correlator involving two
chiral and two anti-chiral operators.Comment: 34 pages, subsection on crossing symmetry adde