Hankel operators on doubling Fock spaces
Hankel operators on doubling Fock spaces
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DOI：
10.1016/j.jmaa.2023.127780
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发表时间：
2023-09
影响因子：
1.3
通讯作者：
Xiaofen Lv;Ermin Wang
中科院分区：
文献类型：
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作者：
Xiaofen Lv;Ermin Wang
假设φ是C上的实值次谐波函数，其中Δ φ为倍量。复倍的Fock空间F φ p是C上满足F(⋅)e−φ(⋅)∈L p的全纯函数族。我们引入了函数空间IDA r s， q, α，并讨论了该空间的分解定理。我们利用它刻画了从倍fok空间F φ p到加权Lesbegue空间L φ q对所有可能的1≤p， q<∞的Hankel算子的有界性和紧性，推广了[9]在ρ−1的特殊情况下的结果。我们还得到了∂∂不要紧算子与Hankel算子的解算子之间的关系。作为一些应用，我们得到了f上Hankel算子H f和H f在f φ p到L φ q之间都是有界的（或紧的）。
Suppose ϕ is a real-valued subharmonic function on C with Δ ϕ d A is a doubling measure. The doubling Fock space F ϕ p is the family of holomorphic functions on C such that f (⋅) e− ϕ (⋅)∈ L p. We introduce the function space IDA r s, q, α and discuss the decomposition theorem for this space. We use it to characterize the boundedness and compactness of Hankel operators from a doubling Fock space F ϕ p to a weighted Lesbegue space L ϕ q for all possible 1≤ p, q<∞, which extends the results of [9] from the special case ρ≍ 1. We also obtain the relationship between the solution operators to∂‾-equation and Hankel operator. As some applications, we obtain the characterizations on f for which Hankel operators H f and H f‾ are both bounded (or compact) from F ϕ p to L ϕ q.