  In this paper, we consider the HKLL bulk reconstruction procedure for
$p$-form fields and graviton in empty AdS$_{d + 1}$. We derive spacelike HKLL
bulk reconstruction kernels for the normalizable and non-normalizable modes of
$p$-forms and graviton in the Poincar\'e patch of AdS$_{d + 1}$. The kernels
are first derived via a mode-sum approach in arbitrary even dimensions. The
appropriate AdS-covariant fields are identified and corresponding kernels
obtained via the mode-sum approach for these fields. We present arguments for
casting these kernels in terms of the AdS chordal distance. Introducing an
antipodal-like mapping, the kernels are cast in a spacelike form. An
alternative derivation is presented for these kernels, by using a chordal
Green's function approach. A derivation of the normalizable mode Green's
function is discussed and a natural choice of the non-normalizable Green's
function is proposed. From the asymptotic expansion of the bulk fields and
using Green's theorem, we read off the spacelike kernels for both modes of
$p$-forms and graviton, which agree with the kernels obtained by the mode-sum
approach. Part of the Appendix is devoted to extending the massless $p$-form
field reconstruction to the massive field, along with comments on the
Brietenlohner-Freedman bound, while part of it is devoted to discussion on the
$p$-form and graviton bulk reconstruction in arbitrary odd dimensional AdS. The
manuscript is concluded with a summary of the main results and some future
directions.
