$L^r$-Multipliers on compact $p$-adic Lie groups

J. P. Velasquez-Rodriguez

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arXiv · 2603.22772

$L^r$-Multipliers on compact $p$-adic Lie groups

J. P. Velasquez-Rodriguez

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Abstract

Let $p$ be a prime number, and let $\mathbb{G}$ be a compact $p$-adic Lie group. This work provides multiplier theorems for invariant operators on $\mathbb{G}$ acting on $L^r_\alpha(\mathbb{G})$, $1 0$, in terms of the Ruzhansky-Turunen difference operators and Saloff-Coste's condition. As an application, a Littlewood-Paley decomposition is proven, together with the $L^r$-boundedness of bounded functions of the Vladimirov-Taibleson operator on compact Vilenkin groups.

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BibTeX RIS

J. P. Velasquez-Rodriguez. 2026-03-24. $L^r$-Multipliers on compact $p$-adic Lie groups. https://arxiv.org/abs/2603.22772

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