  As a tool for solving the Neumann problem for divergence form equations,
Kenig and Pipher introduced the space X of functions on the half space, such
that the non-tangential maximal function of their L_2-Whitney averages belongs
to L_2 on the boundary. In this paper, answering questions which arose from
recent studies of boundary value problems by Auscher and the second author, we
find the pre-dual of X, and characterize the pointwise multipliers from X to
L_2 on the half space as the well-known Carleson-type space of functions
introduced by Dahlberg. We also extend these results to L_p generalizations of
the space X. Our results elaborate on the well-known duality between Carleson
measures and non-tangential maximal functions.
