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Muckenhoupt weights for the Hardy-Littlewood maximal operator on hyperbolic spaces
Abstract
On the real hyperbolic space ℍn, the classical Muckenhoupt condition does not describe the weights w for which the Hardy-Littlewood maximal operator M is bounded on Lp(w). We show that, for 1<p<∞, M is bounded on Lp(w) if and only if w is a local Ap weight and satisfies a two-layer condition, which compares w and its dual weight on two layers of the shadow of a point. We also treat the weak type case, radial weights and the range p≤1, and we prove a weighted Herz principle for radial convolution operators.
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BibTeX
@misc{rana2026muckenhoupt,
title = {{Muckenhoupt weights for the Hardy-Littlewood maximal operator on hyperbolic spaces}},
author = {Tapendu Rana},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26818},
eprint = {2610.26818},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26818},
}
RIS
TY - UNPB
TI - Muckenhoupt weights for the Hardy-Littlewood maximal operator on hyperbolic spaces
AU - Tapendu Rana
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26818
UR - https://arxiv.org/abs/2610.26818
AB - On the real hyperbolic space ℍ^n, the classical Muckenhoupt condition does not describe the weights w for which the Hardy-Littlewood maximal operator M is bounded on L^p(w). We show that, for 1<p<∞, M is bounded on L^p(w) if and only if w is a local A_p weight and satisfies a two-layer condition, which compares w and its dual weight on two layers of the shadow of a point. We also treat the weak type case, radial weights and the range p≤1, and we prove a weighted Herz principle for radial convolution operators.
ER -