The sharp L^p bound for the imaginary part of the Beurling-Ahlfors operator on the lattice

@misc{domelevo2026sharp,
  title = {{The sharp $L^p$ bound for the imaginary part of the Beurling-Ahlfors operator on the lattice}},
  author = {Komla Domelevo and Stefanie Petermichl},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.13573},
  eprint = {2609.13573},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.13573},
}

TY  - UNPB
TI  - The sharp L^p bound for the imaginary part of the Beurling-Ahlfors operator on the lattice
AU  - Komla Domelevo
AU  - Stefanie Petermichl
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.13573
UR  - https://arxiv.org/abs/2609.13573
AB  - We prove the sharp ℓ^p bound p^⋆−1 for certain second-order discrete Riesz transforms on products of integers, in all dimensions. The family includes the imaginary part of the discrete Beurling-Ahlfors operator in dimension two as a special case. While these operators admit a martingale representation via compound Poisson jump processes and heat extensions, the martingale attached to a function and the martingale attached to its transform do not enjoy strong differential subordination, so the operator-norm estimate is not accessible through prior work.
ER  -