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arXiv · 2502.20739

Lacunary Spherical Maximal Operators on Hyperbolic Spaces

Yunxiang Wang·Hong-Wei Zhang
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Abstract

We prove that the lacunary spherical maximal operator, defined on the $n$-dimensional real hyperbolic space, is bounded on $L^p(\H^n)$ for all $n\ge2$ and $1<p\le\infty$. In particular, the lacunary set is significantly larger than its Euclidean counterpart, reflecting the influence of the geometry at infinity of the hyperbolic space.

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Yunxiang Wang, Hong-Wei Zhang. 2025-02-28. Lacunary Spherical Maximal Operators on Hyperbolic Spaces. https://doi.org/10.1007/s00209-026-04055-y

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