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arXiv · 2610.26818

Muckenhoupt weights for the Hardy-Littlewood maximal operator on hyperbolic spaces

Tapendu Rana
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Abstract

On the real hyperbolic space $\mathbb{H}^n$, 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 $1<p<\infty$, $M$ 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 $p\le1$, and we prove a weighted Herz principle for radial convolution operators.

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Tapendu Rana. 2026-10-19. Muckenhoupt weights for the Hardy-Littlewood maximal operator on hyperbolic spaces. https://arxiv.org/abs/2610.26818

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