On the setting of the half-space Rn-1 x R+, we investigate Gleason's proble
m for harmonic Bergman and Bloch functions. We prove that Gleason's problem
for the harmonic L-P-Bergman space is solvable if and only if p > n. We al
so prove that Gleason's problem for the harmonic (little) Bloch space is so
lvable.