n维广义Fock空间Fφp上的Hankel算子
Hankel Operators on n-Dimension Generalized Fock Spaces Fφp
DOI: 10.12677/PM.2022.123037, PDF, HTML, 下载: 405  浏览: 1,571  国家自然科学基金支持
作者: 郝丽丽, 李海绸：华南农业大学数学与信息学院，广东 广州
关键词: Fock空间；Hankel算子；有界性；紧性；Fock Spaces； Hankel Operators； Boundedness； Compactness
摘要: 对于1≤ p < ∞ ，利用有界 (消失) 平均震荡函数的性质，本文讨论了一类 n 维广义 Fock 空间Fφp上的 Hankel 算子Hf和 Hf的有界性和紧性。其中权函数φ∈C2(ℂn)且在流的意义下满足ddcφ≅ω0。同时,利用Berezin变换刻画了空间 BMO 和 VMO 的几何性质。
Abstract: For 1 ≤ p < ∞, we characterize the boundedness and compactness of Hankel operators Hf and Hf on n-dimensional generalized Fock spaces Fφp in terms of the properties of bounded (vanishing) mean oscillation function, where the weight function φ∈C2(ℂn) and satisfies ddcφ≅ω0 in the sense of current. We also give geometric descriptions for the spaces BMO and VMO which are defined in terms of the Berezin transform.
文章引用：郝丽丽, 李海绸. n维广义Fock空间Fφp上的Hankel算子[J]. 理论数学, 2022, 12(3): 323-343. https://doi.org/10.12677/PM.2022.123037

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