L^p properties of non-Archimedean fractional differentiation operators

2021/07/02 by Kochubei, Anatoly N. · 2 citations
#34A08 #35S05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Primary: 47G30. Secondary: 11S80

paper · doi:10.48550/arxiv.2107.00889

Abstract

Let D^α, α>0, be the Vladimirov-Taibleson fractional differentiation operator acting on complex-valued functions on a non-Archimedean local field. The identity D^αD^-αf=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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• Non-Archimedean Kelvin Transformation
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