NOTES ON α-BLOCH SPACE AND Dp(µ)

Abstract

In this paper, we will show that if µ is a Borel measure on the unit disk D such that (1−|z|2)pα < ∞ where 0 < α, p < ∞, then a bounded sequence of functions {fn} in the α-Bloch space Bα has a convergent subsequence in the space Dp(µ) of analytic functions f on D satisfying f ' ∈ Lp(D, µ). Also, we will find some conditions such that

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