Let $ 1\leq p < \infty $, $ 0 < \lambda\leq2 $, and $ \alpha > 0 $. This paper provides a four-case classification of the boundedness and compactness of composition operators from the Bloch space $ \mathcal{B} $ into the $ \alpha $–Bergman–Morrey space $ A^{p, \lambda, \alpha} $. Quantitative integral criteria for boundedness and compactness of such operators are also derived. As a corollary, we obtain a new integral description for the compactness of $ C_\phi:\mathcal{B}\to \mathcal{B} $.
Citation: Xiangling Zhu, Qinghua Hu. Composition operators from the Bloch space to $ \alpha $-Bergman–Morrey spaces[J]. AIMS Mathematics, 2026, 11(9): 30815-30829. doi: 10.3934/math.20261220
Let $ 1\leq p < \infty $, $ 0 < \lambda\leq2 $, and $ \alpha > 0 $. This paper provides a four-case classification of the boundedness and compactness of composition operators from the Bloch space $ \mathcal{B} $ into the $ \alpha $–Bergman–Morrey space $ A^{p, \lambda, \alpha} $. Quantitative integral criteria for boundedness and compactness of such operators are also derived. As a corollary, we obtain a new integral description for the compactness of $ C_\phi:\mathcal{B}\to \mathcal{B} $.
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Xiangling Zhu, Qinghua Hu. Composition operators from the Bloch space to $ \alpha $-Bergman–Morrey spaces[J]. AIMS Mathematics, 2026, 11(9): 30815-30829. doi: 10.3934/math.20261220
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