Abstract
Suppose 0<p≤∞ and −∞<α<∞. Let ℬℋp,α denote the logarithmic Hardy–Bloch type space of those functions f which are analytic in the unit disk 𝔻 such that ∥f∥p,α=sup|z|<1(1−|z|)(loge1−|z|)αMp(|z|,f′)<∞. In this paper, we mainly obtain the relation between the logarithmic Hardy–Bloch type space ℬℋp,α and the Hardy space Hp (or the Dirichlet space 𝒟p−1p). We also give the characterization of lacunary series on ℬℋp,α when 1<p≤∞.
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