加权BMOA空间上加权复合算子的紧性及相关性质

IF 1.3 3区数学 Q2 MATHEMATICS, APPLIED

Bulletin des Sciences Mathematiques Pub Date : 2025-04-17 DOI:10.1016/j.bulsci.2025.103642

David Norrbo

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引用次数: 0

摘要

结果表明，在一大类加权VMOA空间上，加权复合算子有一大类性质重合，包括对数权算子和标准权算子(1−|z|)−c,0≤c<12。这些性质包括紧性、弱紧性、完全连续性和严格奇异性。并给出了这些性质的泛函理论表征。对于类似加权BMOA空间上的许多加权复合算子也证明了类似的结果。主要结果推广了Laitila et al.(2023)[16]中给出的定理，并开发了适用于加权设置的新测试函数。

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Compactness and related properties of weighted composition operators on weighted BMOA spaces

It is shown that a large class of properties coincide for weighted composition operators on a large class of weighted VMOA spaces, including the ones with logarithmic weights and the ones with standard weights

{(1 - | z |)}^{- c}, 0 \leq c < \frac{1}{2}

. Some of these properties are compactness, weak compactness, complete continuity and strict singularity. A function-theoretic characterization for these properties is also given. Similar results are also proved for many weighted composition operators on similarly weighted BMOA spaces. The main results extend the theorems given in Laitila et al. (2023) [16], and new test functions that are suitable for the weighted setting are developed.

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