Toeplitz and Hankel operators on Bergman spaces with doubling weights

@misc{duan2026toeplitz,
  title = {{Toeplitz and Hankel operators on Bergman spaces with doubling weights}},
  author = {Yongjiang Duan and Kunyu Guo and Junhan Hong and Fugang Yan},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.23402},
  eprint = {2609.23402},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.23402},
}

TY  - UNPB
TI  - Toeplitz and Hankel operators on Bergman spaces with doubling weights
AU  - Yongjiang Duan
AU  - Kunyu Guo
AU  - Junhan Hong
AU  - Fugang Yan
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2609.23402
UR  - https://arxiv.org/abs/2609.23402
AB  - In this paper, we focus on the boundedness and compactness of the Toeplitz operators and the Hankel operators on the 𝒟-weighted Bergman spaces A_ω^p (1≤ p<∞). In particular, the boundedness of Toeplitz operators with BMO_ω^p-symbols on A_ω^p is characterized in terms of the Berezin-type transform. Several sufficient conditions for the Toeplitz operators T_f^ω with locally integrable symbols to be bounded (resp. compact) for each 1≤ p<∞ are presented. Moreover, sufficient and necessary conditions for the boundedness of the Toeplitz operator T_f̅^ω:A_ω^1→ A_ω^1 and the Hankel operator H_f̅^ω:A_ω^1→ L_ω^1 with co-analytic symbol are established.
ER  -