论文标题
Vladimirov-Taibleson操作员：不平等，Dirichlet问题，边界Hölder规律性
The Vladimirov-Taibleson Operator: Inequalities, Dirichlet Problem, Boundary Hölder Regularity
论文作者
论文摘要
我们研究Vladimirov-Taibleson操作员，这是作用于在非Archimedean局部场上定义的实现或复杂值函数的伪差异操作员的模型示例。我们证明了分数laplacian的经典不平等现象的类似物，研究了Dirichlet问题的对应物，包括边界Hölder规律性解决方案的特性。
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.
