Norms of the Hilbert Matrix Operator on Some Analytic Function Spaces

@misc{cui2026norms,
  title = {{Norms of the Hilbert Matrix Operator on Some Analytic Function Spaces}},
  author = {Puyu Cui and Zhaopeng Lin and Yufeng Lu and Shanli Ye},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.27812},
  eprint = {2609.27812},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.27812},
}

TY  - UNPB
TI  - Norms of the Hilbert Matrix Operator on Some Analytic Function Spaces
AU  - Puyu Cui
AU  - Zhaopeng Lin
AU  - Yufeng Lu
AU  - Shanli Ye
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.27812
UR  - https://arxiv.org/abs/2609.27812
AB  - For ℋ:ℬ^α→ℬ^α with 1<α<2, we obtain an exact norm representation. In particular, the norm is given by an explicit Gamma-function formula for 1<α≤3/2, whereas for 3/2<α<2 it strictly exceeds the corresponding Gamma-function expression. For ℋ:ℬ^α→ℬ^α_log, we determine the exact norm: it is equal to 3/2 for 1<α≤4/3 and is given by an explicit Gamma-function formula for 4/3<α<2. We also determine the exact norm of ℋ:H^1→ H^1_log and show that it is equal to π. Finally, for 0<α<1, we determine the exact norm of ℋ:H^∞_α→ℬ^α+1, which is given by an explicit Gamma-function formula.
ER  -