$L^r$-Multipliers on compact $p$-adic Lie groups
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908909031129088 |
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| author | Velasquez-Rodriguez, J. P. |
| author_facet | Velasquez-Rodriguez, J. P. |
| contents | 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 $L^r_α(\mathbb{G})$, $1<r<\infty$, $α>0$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_22772 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $L^r$-Multipliers on compact $p$-adic Lie groups Velasquez-Rodriguez, J. P. Representation Theory Rings and Algebras 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 $L^r_α(\mathbb{G})$, $1<r<\infty$, $α>0$, 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. |
| title | $L^r$-Multipliers on compact $p$-adic Lie groups |
| topic | Representation Theory Rings and Algebras |
| url | https://arxiv.org/abs/2603.22772 |