发表机构
School of Science, Nanjing Forestry University; School of Mathematics and Statistics, Tianshui Normal University（南京林业大学理学院; 天水师范学院数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究加权Fock空间上复符号Toeplitz算子的绝对r-求和性，通过IDA分解和Rademacher论证等工具，给出了基于局部均值、复球平均和Berezin变换的等价刻画，并证明了准则的最优性。
AI 中文摘要
我们研究具有复值符号的绝对$r$-求和Toeplitz算子$T_f:F_\varphi^p\to F_\varphi^q$。权重具有一致正且有界的实Hessian。主要困难在于到全纯函数的局部距离无法检测符号的整个部分，而Toeplitz算子却能检测到。利用绝对求和对角映射的完整分类，我们刻画了绝对求和的Fock-Carleson嵌入。一个IDA分解、一个Rademacher论证以及局部标量恢复随后检测出复符号中缺失的解析部分。对于每个$1\le p,q,r<\infty$，我们获得了等价准则，涉及局部$L^q$均值、复球平均和Berezin变换。在$q=1$时，准则为$L^{s_p}$，其中当$p\le2$时$s_p=2p/(3p-2)$，当$p>2$时$s_p=1$。我们还获得了无需IDA假设的扇形符号准则，并通过分离模型证明了其最优性。
英文摘要
We study absolutely $r$-summing Toeplitz operators $T_f:F_φ^p\to F_φ^q$ with complex symbols. The weight has a uniformly positive and bounded real Hessian. The main difficulty is that local distance to holomorphic functions does not detect an entire part of the symbol, while the Toeplitz operator does. Using the complete classification of absolutely summing diagonal maps, we characterize absolutely summing Fock--Carleson embeddings. An IDA decomposition, a Rademacher argument, and local scalar recovery then detect the missing analytic part of a complex symbol. We obtain equivalent criteria in terms of the local $L^q$ mean, the complex ball average, and the Berezin transform for every $1\le p,q,r<\infty$. At $q=1$ the criterion is $L^{s_p}$, where $s_p=2p/(3p-2)$ for $p\le2$ and $s_p=1$ for $p>2$. We also obtain a sectorial-symbol criterion without an IDA assumption and prove sharpness by separated models.
