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arXiv · 2107.00889

$L^p$ properties of non-Archimedean fractional differentiation operators

Anatoly N. Kochubei
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Abstract

Let $D^\alpha, \alpha>0$, be the Vladimirov-Taibleson fractional differentiation operator acting on complex-valued functions on a non-Archimedean local field. The identity $D^\alpha D^{-\alpha}f=f$ was known only for the case where $f$ has a compact support. Following a result by Samko about the fractional Laplacian of real analysis, we extend the above identity in terms of $L^p$-convergence of truncated integrals. Differences between real and non-Archimedean cases are discussed.

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Anatoly N. Kochubei. 2021-07-02. $L^p$ properties of non-Archimedean fractional differentiation operators. https://arxiv.org/abs/2107.00889

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