Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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MULTIPLIERS OF DIRICHLET-TYPE SUBSPACES OF BLOCH SPACE

  • Received : 2019.03.18
  • Accepted : 2019.10.16
  • Published : 2020.03.31
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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 Dirichlet-type spaces 𝓓αp, M(𝓓p-1p, 𝓓q-1q) = {0}, if p ≠ q, 0 < p, q < ∞. If 0 < p, q < ∞, p ≠ q, 0 < s < 1 such that p + s, q + s > 1, then M(𝓓p-2+sp, 𝓓q-2+sq) = {0}. However, X ∩ 𝓓p-1p ⊆ X ∩ 𝓓q-1q and X ∩ 𝓓p-2+sp ⊆ X ∩ 𝓓q-2+sp 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+sp, X∩𝓓q-2+sq) is nontrivial. In this paper, we study the multipliers M(X ∩ 𝓓p-2+sp, X ∩ 𝓓q-2+sq) for distinct classical subspaces X of the Bloch space 𝓑, where X = 𝓑, BMOA or 𝓗∞.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China

The research was supported by the National Natural Science Foundation of China (Nos.11571217, 11720101003, 11871293) and Key Projects of Fundamental Research in Universities of Guangdong Province (No.2018KZDXM034).

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