  Christ and Kiselev have established that the generalized eigenfunctions of
one-dimensional Dirac operators with $L^p$ potential $F$ are bounded for almost
all energies for $p < 2$. Roughly speaking, the proof involved writing these
eigenfunctions as a multilinear series $\sum_n T_n(F, ..., F)$ and carefully
bounding each term $T_n(F, ..., F)$. It is conjectured that the results of
Christ and Kiselev also hold for $L^2$ potentials $F$. However in this note we
show that the bilinear term $T_2(F,F)$ and the trilinear term $T_3(F,F,F)$ are
badly behaved on $L^2$, which seems to indicate that multilinear expansions are
not the right tool for tackling this endpoint case.
