伯格曼和布洛赫空间上 Volterra 算子的一些算子理想特性

Pub Date : 2023-12-10 DOI:10.1007/s00020-023-02742-7

Joelle Jreis, Pascal Lefèvre

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引用次数: 0

摘要

我们描述了符号为 g 的积分算子 \(V_g\)，对于这些算子，\(V_g\) 在加权布洛赫空间 \(\mathcal {B}^{\beta }\) 和加权伯格曼空间 \(\mathscr {A}^p_\alpha \)上作为绝对求和算子。我们证明，当且仅当g属于一个合适的贝索夫空间时，\(V_g\)在\(\mathscr {A}^p_\alpha \)、\(1 \le p <\infty \)上是r求和的。我们还证明了在布洛赫空间和贝格曼空间上不存在非微不足道的核 Volterra 算子 \(V_g\)。

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Some Operator Ideal Properties of Volterra Operators on Bergman and Bloch Spaces

We characterize the integration operators \(V_g\) with symbol g for which \(V_g\) acts as an absolutely summing operator on weighted Bloch spaces \(\mathcal {B}^{\beta }\) and on weighted Bergman spaces \(\mathscr {A}^p_\alpha \). We show that \(V_g\) is r-summing on \(\mathscr {A}^p_\alpha \), \(1 \le p <\infty \), if and only if g belongs to a suitable Besov space. We also show that there is no non trivial nuclear Volterra operators \(V_g\) on Bloch spaces and on Bergman spaces.

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