Abstract: In the paper, the author will discuss the multiplier problem on generalized little Bloch space and Gleason's problem on generalized Bloch space in the unit ball of Cⁿ. The following results are obtained: ( 1) Gleason's result is true on p - Bloch space; ( 2) if 0 ≤ p< 1, then M( β^p₀) =β^p₀; ( 3) if p> 1, then M( β^p₀) = H
.

Key words: p- Bloch space, pointwise multiplier, unit ball, Gleasoncs problem