IDA符号与加权Fock空间上Toeplitz算子的Schatten--Lorentz理论
IDA symbols and Schatten--Lorentz theory for Toeplitz operators on weighted Fock spaces
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中文总结 AI 辅助
本文研究加权Fock空间上Toeplitz算子的Schatten--Lorentz类成员资格，通过局部解析距离与Lorentz条件给出完整刻画，并推导出二次权情形的显式Weyl常数。
中文摘要 AI 辅助
我们研究加权Fock空间上复符号的Toeplitz算子。权函数的实Hessian矩阵一致正定且有界。当在符号上加上一个整函数时，局部解析距离保持不变。我们将此距离与复球平均或Berezin变换结合，以控制符号的局部大小。在距离满足相应的Lorentz条件下，我们刻画了每个Schatten--Lorentz类中的成员资格。局部符号指数可以是任意$1\le q<\infty$，并且与两个Schatten--Lorentz指数无关。证明使用了正Toeplitz估计、Hankel估计以及保持初始定义域的局部分解。两个例子说明了为何必须保留局部指数和次级Lorentz指数。我们还获得了混合映射准则和正则奇异值衰减估计。具有低阶计数函数的误差算子不会改变首项系数。这为二次权给出了显式的Weyl常数。一个径向例子表明，仅有一致的Hessian界并不能推出这样的常数。
英文摘要
We study complex-symbol Toeplitz operators on weighted Fock spaces. The weight has a uniformly positive and bounded real Hessian. Local analytic distance is unchanged when an entire function is added to the symbol. We combine this distance with a complex ball average or the Berezin transform to control the local size of the symbol. Under a matching Lorentz condition on the distance, we characterize membership in every Schatten--Lorentz class. The local symbol exponent can be any $1\le q<\infty$ and is independent of the two Schatten--Lorentz indices. The proof uses positive Toeplitz estimates, Hankel estimates, and a local decomposition that preserves the initial domain. Two examples show why the local exponent and the secondary Lorentz index must be kept. We also obtain mixed mapping criteria and regular singular-value decay estimates. An error operator with a lower-order counting function does not change the leading coefficient. This gives explicit Weyl constants for quadratic weights. A radial example shows that uniform Hessian bounds alone do not imply such a constant.
发表机构
- Nanjing Forestry University（南京林业大学）
- Tianshui Normal University（天水师范学院）
机构由 AI 辅助整理，请以论文原文为准。
