MULTIPLIERS OF DIRICHLET-TYPE SUBSPACES OF BLOCH SPACE

Abstract

Let M(X,Y ) denote the space of multipliers from X to Y, where X and Y are analytic function spaces. As we known, for Dirichlettype spaces D α, M(D p−1,D q q−1) = {0}, if p 6= q, 0 < p, q < ∞. If 0 < p, q < ∞, p 6= q, 0 < s < 1 such that p + s, q + s > 1, then M(D p−2+s,D q q−2+s) = {0}. However, X ∩ D p p−1 ⊆ X ∩ D q q−1 and X ∩ D p−2+s ⊆ X ∩ D q q−2+s whenever X is a subspace of the Bloch space B and 0 < p ≤ q < ∞. This says that the set of multipliers M(X ∩ D p−2+s, X∩D q q−2+s) is nontrivial. In this paper, we study the multipliers M(X ∩ D p−2+s, X ∩ D q q−2+s) for distinct classical subspaces X of the Bloch space B, where X = B, BMOA or H∞.