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PreprintarXiv licencearXiv

Optimal distributional estimates of the multiple Hilbert transform

  • F. Sukochev
  • K. Tulenov
  • D. Zanin
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Abstract

In this paper, we study optimal distributional estimates for the multiple Hilbert transform. We obtain pointwise upper and lower distributional estimates of the multiple Hilbert transform in terms of the d-fold composition of the Calderón operator with itself. This extends the fundamental results by A. P. Calderón, D. Boyd, and Ch. Fefferman for arbitrary d∈ℕ.

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Cite

BibTeXRIS
BibTeX
@misc{sukochev2026optimal,
  title = {{Optimal distributional estimates of the multiple Hilbert transform}},
  author = {F. Sukochev and K. Tulenov and D. Zanin},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.02910},
  eprint = {2606.02910},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.02910},
}
RIS
TY  - UNPB
TI  - Optimal distributional estimates of the multiple Hilbert transform
AU  - F. Sukochev
AU  - K. Tulenov
AU  - D. Zanin
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2606.02910
UR  - https://arxiv.org/abs/2606.02910
AB  - In this paper, we study optimal distributional estimates for the multiple Hilbert transform. We obtain pointwise upper and lower distributional estimates of the multiple Hilbert transform in terms of the d-fold composition of the Calderón operator with itself. This extends the fundamental results by A. P. Calderón, D. Boyd, and Ch. Fefferman for arbitrary d∈ℕ.
ER  -