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PreprintCC BY 4.0arXiv

Endpoint estimates for spherical maximal operators acting on radial functions in hyperbolic spaces

  • Yunxiang Wang
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Abstract

In this article we investigate spherical maximal operators mα of real order α acting on radial functions in the hyperbolic space ℍn. We show that for every n≥ 2, 1<p≤∞ and α>(1−n)/2, mα is bounded on Lprad(ℍn) if and only if α>1−n+n/p, & 1<p≤ 2, α>1/p−(n−1)/2, & 2<p≤2n/(n−1), α≥(1−n)/p, & p>2n/(n−1). Moreover, we show that for 1<p≤ 2n/(n−1) and α= 1−n+n/p, & 1<p≤ 2, 1/p−(n−1)/2, & 2<p≤2n/(n−1), mα is bounded from Lp,1rad(ℍn) to Lp,∞rad(ℍn).

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Cite

BibTeXRIS
BibTeX
@misc{wang2026endpoint,
  title = {{Endpoint estimates for spherical maximal operators acting on radial functions in hyperbolic spaces}},
  author = {Yunxiang Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38168},
  eprint = {2610.38168},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38168},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Endpoint estimates for spherical maximal operators acting on radial functions in hyperbolic spaces
AU  - Yunxiang Wang
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.38168
UR  - https://arxiv.org/abs/2610.38168
AB  - In this article we investigate spherical maximal operators m^α of real order α acting on radial functions in the hyperbolic space ℍ^n. We show that for every n≥ 2, 1<p≤∞ and α>(1−n)/2, m^α is bounded on L^p_rad(ℍ^n) if and only if α>1−n+n/p, & 1<p≤ 2, α>1/p−(n−1)/2, & 2<p≤2n/(n−1), α≥(1−n)/p, & p>2n/(n−1). Moreover, we show that for 1<p≤ 2n/(n−1) and α= 1−n+n/p, & 1<p≤ 2, 1/p−(n−1)/2, & 2<p≤2n/(n−1), m^α is bounded from L^p,1_rad(ℍ^n) to L^p,∞_rad(ℍ^n).
ER  -