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arXiv · 2209.07998

The Vladimirov-Taibleson Operator: Inequalities, Dirichlet Problem, Boundary Hölder Regularity

Anatoly N. Kochubei
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Abstract

We study the Vladimirov-Taibleson operator, a model example of a pseudo-differential operator acting on real- or complex-valued functions defined on a non-Archimedean local field. We prove analogs of classical inequalities for fractional Laplacian, study the counterpart of the Dirichlet problem including the property of boundary Hölder regularity of solutions.

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Anatoly N. Kochubei. 2023-04-09. The Vladimirov-Taibleson Operator: Inequalities, Dirichlet Problem, Boundary Hölder Regularity. https://arxiv.org/abs/2209.07998

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