Small exponent Schatten class Toeplitz operators on convex domains of finite type

@misc{li2026small,
  title = {{Small exponent Schatten class Toeplitz operators on convex domains of finite type}},
  author = {Mingjin Li and Jianren Long and Lang Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.22908},
  eprint = {2609.22908},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.22908},
}

TY  - UNPB
TI  - Small exponent Schatten class Toeplitz operators on convex domains of finite type
AU  - Mingjin Li
AU  - Jianren Long
AU  - Lang Wang
PY  - 2026
DA  - 2026/09/19
PB  - arXiv
DO  - 10.48550/arxiv.2609.22908
UR  - https://arxiv.org/abs/2609.22908
AB  - In this paper, we study the characterizations of Schatten p-class Toeplitz operators on smoothly bounded convex domains of finite type in C^n. On one hand, by using discrete Kobayashi lattice, we characterize the Schatten p-class Toeplitz operators by employing a probabilistic selection method for 0<p<1. At the same time, we show that the characterizations obtained by Kobayashi lattice are equivalent to the Berezin transform for p > n/(n+1). On the other hand, as an application, the criterion gives a geometric characterization for Schatten p-class weighted composition operators for 0<p<2 and also gives an analytic characterization for p>2n/(n+1). Our main results give an answer to the question that find a geometric or analytic characterization of the Schatten p-class weighted composition operators whenever 0<p<2 raised by Xiao-Yang-Yuan \cite{Xiao2026}.
ER  -