We study composition operators Cφ between the Hardy space Hp and the Bergman spaces Lqa, between the Besov type space Bp, p-1 and the Bergman spaces Lqa. Using the main results in this paper, as a result, we can also prove the following: If 0 < q ≤ p, then Cφ: Hp →Lqa is bounded, while there is no symbol φ such that it is bounded below.
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Rikio Yoneda (2024) studied this question.
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