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Bilinear maximal functions associated with some degenerate surfaces on the Heisenberg group

  • Sayan Bagchi
  • Rahul Garg
  • Surya Kanta Rana
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Abstract

Motivated by the works of Lee--Shuin and Borges--Foster on the Euclidean space, in this article we consider bilinear averages on the Heisenberg group ℍn corresponding to some degenerate surfaces associated with the Korányi norm as well as Nevo--Thangavelu type averaging structures, and study the boundedness of the their full and lacunary maximal functions on various Lp(ℍn) × Lq(ℍn) spaces, for n ≥ 2. For the full maximal functions, we obtain optimal range except possibly at the end points.

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Cite

BibTeXRIS
BibTeX
@misc{bagchi2026bilinear,
  title = {{Bilinear maximal functions associated with some degenerate surfaces on the Heisenberg group}},
  author = {Sayan Bagchi and Rahul Garg and Surya Kanta Rana},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.02745},
  eprint = {2611.02745},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.02745},
}
RIS
TY  - UNPB
TI  - Bilinear maximal functions associated with some degenerate surfaces on the Heisenberg group
AU  - Sayan Bagchi
AU  - Rahul Garg
AU  - Surya Kanta Rana
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.02745
UR  - https://arxiv.org/abs/2611.02745
AB  - Motivated by the works of Lee--Shuin and Borges--Foster on the Euclidean space, in this article we consider bilinear averages on the Heisenberg group ℍ^n corresponding to some degenerate surfaces associated with the Korányi norm as well as Nevo--Thangavelu type averaging structures, and study the boundedness of the their full and lacunary maximal functions on various L^p(ℍ^n) × L^q(ℍ^n) spaces, for n ≥ 2. For the full maximal functions, we obtain optimal range except possibly at the end points.
ER  -