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arXiv · 2610.04463

Sharp Hardy inequalities for the Vladimirov--Taibleson operator on $\mathbb{Q}_p^n$

Yaojia Sun
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Abstract

We prove sharp Hardy inequalities on $\mathbb{Q}_p^n$ for the quadratic form of the Vladimirov--Taibleson operator, the $L^q$ norm of its fractional derivative, and a nonlinear difference energy. Under the self-dual Fourier normalization, the sharp quadratic-form constant for $0<α 0$. The Hardy inequalities on the full test-function space therefore hold precisely when $sq<n$, without the restriction $s<1$.

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Yaojia Sun. 2026-10-03. Sharp Hardy inequalities for the Vladimirov--Taibleson operator on $\mathbb{Q}_p^n$. https://arxiv.org/abs/2610.04463

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