Abstract. For 0 < p < ∞, α > −1 and 0 < r < 1, we show that if f is in the space of Dirichlet type. For 1 < p < q < ∞ and α + 1 < p, we show that if there exists some positive constant c such thatwhere Bp(g) is the weighted Besov space. We also find the condition of measure µ such that sup a∈D D (k a (z)(1 − |a| 2 ) (p−α−1) ) q/p dµ(z) < ∞.