2024, Vol. 9, Issue 2, Part B

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