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Spherical maximal operators on rank one Riemannian symmetric spaces of noncompact type
Abstract
The spherical maximal operator of order μ was introduced by El Kohen in the setting of real hyperbolic spaces, where its Lp-boundedness properties were studied. In this paper, we extend this notion to rank-one Riemannian symmetric spaces of noncompact type. We establish sufficient conditions on the parameter μ for the corresponding spherical maximal operator to be bounded on Lp for 1<p≤∞. We also obtain a necessary condition for Lp-boundedness when μ is real and 1<p<∞. In particular, for 1<p≤2, the necessary condition agrees with the sufficient condition, yielding the sharp range of real μ in this regime.
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BibTeX
@misc{dakshi2026spherical,
title = {{Spherical maximal operators on rank one Riemannian symmetric spaces of noncompact type}},
author = {Subir Dakshi and Sanjoy Pusti},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15514},
eprint = {2609.15514},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15514},
}
RIS
TY - UNPB
TI - Spherical maximal operators on rank one Riemannian symmetric spaces of noncompact type
AU - Subir Dakshi
AU - Sanjoy Pusti
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15514
UR - https://arxiv.org/abs/2609.15514
AB - The spherical maximal operator of order μ was introduced by El Kohen in the setting of real hyperbolic spaces, where its L^p-boundedness properties were studied. In this paper, we extend this notion to rank-one Riemannian symmetric spaces of noncompact type. We establish sufficient conditions on the parameter μ for the corresponding spherical maximal operator to be bounded on L^p for 1<p≤∞. We also obtain a necessary condition for L^p-boundedness when μ is real and 1<p<∞. In particular, for 1<p≤2, the necessary condition agrees with the sufficient condition, yielding the sharp range of real μ in this regime.
ER -