  For continuous boundary data, including data of polynomial growth, modified
Poisson integrals are used to write solutions to the half space Dirichlet and
Neumann problems in $\mathbb{R}^{n}$. Pointwise growth estimates for these
integrals are given and the estimates are proved sharp in a strong sense. For
decaying data, a new type of modified Poisson integral is introduced and used
to develop asymptotic expansions for solutions of these half space problems.
