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PreprintCC BY 4.0arXiv

On pointwise convergence of singular integrals of Christ-Journé type

  • Ankit Bhojak
  • Sangita Kundu
  • Saurabh Shrivastava
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Abstract

The primary objective of this paper is to establish the pointwise almost everywhere convergence of the singular integrals of Christ-Journé type. To this end, we prove the weak type (1,1) estimate for the corresponding maximal operator defined as T*[a] f(x):= supr>0|∫|x−y| > r K(x−y) ∫01 a(tx + (1−t)y) dt f(y) dy|, where K is a Calderón--Zygmund kernel and a∈ L∞. This result resolves a problem posed by Seeger (Rev. Mat. Iberoam., 2014).

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Cite

BibTeXRIS
BibTeX
@misc{bhojak2026pointwise,
  title = {{On pointwise convergence of singular integrals of Christ-Journé type}},
  author = {Ankit Bhojak and Sangita Kundu and Saurabh Shrivastava},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.04673},
  eprint = {2610.04673},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.04673},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On pointwise convergence of singular integrals of Christ-Journé type
AU  - Ankit Bhojak
AU  - Sangita Kundu
AU  - Saurabh Shrivastava
PY  - 2026
DA  - 2026/10/03
PB  - arXiv
DO  - 10.48550/arxiv.2610.04673
UR  - https://arxiv.org/abs/2610.04673
AB  - The primary objective of this paper is to establish the pointwise almost everywhere convergence of the singular integrals of Christ-Journé type. To this end, we prove the weak type (1,1) estimate for the corresponding maximal operator defined as T^*[a] f(x):= sup_r>0|∫_|x−y| > r K(x−y) ∫_0^1 a(tx + (1−t)y) dt f(y) dy|, where K is a Calderón--Zygmund kernel and a∈ L^∞. This result resolves a problem posed by Seeger (Rev. Mat. Iberoam., 2014).
ER  -