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- W4381853641 abstract "We utilize the (Aαp,q)-Carleson measure to investigate the bounded small Hankel operator hfα acting between the Bergman-type space Aαp and Aαq¯ on the complex unit ball Bn for some α≤−1. For n≥2, and f∈H(Bn), we have the conclusions: Suppose α≤−1, max{1,−2α−2}<p<∞ and pN+α>−1. Then hfα:Aαp→Aαp¯ is bounded if and only if |RNf(z)|pdvpN+α(z) is an (Aαp,p)-Carleson measure.Suppose −n−1<α≤−1, max{1,−2α−2}<p<q<∞ and pN>max{q−pp(n+1+α)−2(α+1),−p(α+1)p−1}. Then hfα:Aαp→Aαq¯ is bounded if and only if |RNf(z)|qdvqN+α(z) is an (Aαp,q)-Carleson measure.Suppose 1<q<p<∞, α≤−1, N be a positive integer such that qN+α>−1. If |RNf(z)|qdvqN+α(z) is an (Aαp,q)-Carleson measure, then hfα:Aαp→Aαq¯ is bounded.Let κ=pqp−q and κ′=κκ−1. If α+(p−1)κ′N>−1 and hfα:Aαp→Aαq¯ is bounded, then f∈Aακ with ‖f‖Aακ≲‖hfα‖.If |RNf(z)|qdvqN+α(z) is an (Aαp,q)-Carleson measure, then f∈Aακ. But, there is an f∈Aακ such that |RNf(z)|qdvqN+α(z) is not an (Aαp,q)-Carleson measure." @default.
- W4381853641 created "2023-06-25" @default.
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- W4381853641 date "2023-06-22" @default.
- W4381853641 modified "2023-09-27" @default.
- W4381853641 title "Small Hankel operators between Bergman-type spaces in the unit ball" @default.
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- W4381853641 doi "https://doi.org/10.1080/17476933.2023.2226060" @default.
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