Sharp growth estimates for modified Poisson integrals in a half space (Q5952186)

The authors use modified Poisson integrals in order to write solutions to the half space Dirichlet and Neumann problems in \({\mathbb R}^n\) with continuous boundary data, including data of polynomial growth. Pointwise growth estimates are given for these integrals which are 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.