Sharp estimates for the gradient of the generalized Poisson integral for a half-space

Abstract

A representation of the sharp coefficient in a pointwise estimate for the gradient of the generalized Poisson integral of a function $f$ on ${\mathbb{R}}^n$ is obtained under the assumption that $f$ belongs to $L^p$. The explicit value of the coefficient is found for the cases $p=1$ and $p=2$.

10 pages