Some Properties of Products of Linear Fractional Composition Operators on Weighted Dirichlet Spaces

@misc{he2026some,
  title = {{Some Properties of Products of Linear Fractional Composition Operators on Weighted Dirichlet Spaces}},
  author = {Li He and Yuanhao Yan and Shuqing Zhang and Xianfeng Zhao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.29897},
  eprint = {2609.29897},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.29897},
}

TY  - UNPB
TI  - Some Properties of Products of Linear Fractional Composition Operators on Weighted Dirichlet Spaces
AU  - Li He
AU  - Yuanhao Yan
AU  - Shuqing Zhang
AU  - Xianfeng Zhao
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.29897
UR  - https://arxiv.org/abs/2609.29897
AB  - We study the Schatten class membership and essential norms of the operators C_φC_ψ^* and C_ψ^*C_φ, where C_φ and C_ψ are composition operators with nonconstant linear fractional symbols, acting on weighted Dirichlet spaces 𝒟_α with α>−1. We obtain complete characterizations of their Schatten class membership in terms of the boundary behavior of φ and ψ. In particular, the corresponding geometric conditions are independent of the Schatten exponent, and each product belongs to every Schatten class whenever its boundary condition is satisfied. We also investigate the essential norms of these products. For α=0 and α>0, we obtain exact formulas in terms of boundary contact and the derivatives of the symbols, while for −1<α<0 we obtain two-sided estimates by reducing the problem to positive Toeplitz operators and local averages of generalized Nevanlinna counting functions.
ER  -