  In this paper, we Fourier transform the Wightman function concerning energy
and angular momentum on the $S^{D-1}$ spatial slice in radial quantization in
$D=2,3$ dimensions. In each case, we use the conformal Ward Identities to solve
systematically for the Fourier components. We then use these Fourier components
to build conformal blocks for the four-point function in momentum space, giving
a finite-volume version of the momentum-space conformal blocks. We check that
this construction is consistent with the known result in infinite volume. Our
construction may help to find bootstrap equations that can give nontrivial
constraints that do not appear in analysis in infinite volume. We show some
examples of bootstrap equations and their nontriviality.
