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PreprintCC BY 4.0arXiv

On Lp bounds for the Littlewood-Paley gα function with fractional poisson kernel

  • Hui Li
  • Ziyuan Lian
  • Honghai Liu
  • Zengyan Si
  • Jie Wang
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Abstract

Let 0<α≤1, and let gα be the Littlewood-Paley function associated with the fractional Poisson kernel, which reduces to the classical g-function when α=1. We establish dimension-free Lp bounds for gα for every 1<p<∞ and identify its exact L2 norm as √(α/2). We further determine the precise asymptotic behavior of the weak-type (1,1) constant as n→∞, yielding quantitative upper and lower bounds in terms of the dimension.

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Cite

BibTeXRIS
BibTeX
@misc{li2026bounds,
  title = {{On $L^p$ bounds for the Littlewood-Paley $g_α$ function with fractional poisson kernel}},
  author = {Hui Li and Ziyuan Lian and Honghai Liu and Zengyan Si and Jie Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.32387},
  eprint = {2609.32387},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.32387},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On L^p bounds for the Littlewood-Paley g_α function with fractional poisson kernel
AU  - Hui Li
AU  - Ziyuan Lian
AU  - Honghai Liu
AU  - Zengyan Si
AU  - Jie Wang
PY  - 2026
DA  - 2026/09/26
PB  - arXiv
DO  - 10.48550/arxiv.2609.32387
UR  - https://arxiv.org/abs/2609.32387
AB  - Let 0<α≤1, and let g_α be the Littlewood-Paley function associated with the fractional Poisson kernel, which reduces to the classical g-function when α=1. We establish dimension-free L^p bounds for g_α for every 1<p<∞ and identify its exact L^2 norm as √(α/2). We further determine the precise asymptotic behavior of the weak-type (1,1) constant as n→∞, yielding quantitative upper and lower bounds in terms of the dimension.
ER  -