Abstract
The paper deals with an extremal problem for bounded harmonic functions in the unit ball of
R
4
. We solve the generalized Khavinson problem in
R
4
. This precise problem was formulated by G. Kresin and V. Maz'ya for harmonic functions in the unit ball and in the half--space of
R
n
. We find the optimal pointwise estimates for the norm of the gradient of bounded real--valued harmonic functions.