Research Article
The Vladimirov-Taibleson Operator: Inequalities, Dirichlet Problem, Boundary H"older Regularity
https://doi.org/10.21203/rs.3.rs-2504116/v1
This work is licensed under a CC BY 4.0 License
published 08 Apr, 2023
Read the published version in Journal of Pseudo-Differential Operators and Applications →
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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 H\"older regularity of solutions.
MSC 2020. Primary: 35S05. Secondary: 11S80, 47G30, 35S11; 35R11.
fractional differentiation operator
non-Archimedean local field
Riesz potentials
Dirichlet problem
boundary regularity
No competing interests reported.
published 08 Apr, 2023
Read the published version in Journal of Pseudo-Differential Operators and Applications →
Editorial decision: Major revision
24 Mar, 2023
Reviews received at journal
22 Mar, 2023
Reviewers agreed at journal
23 Jan, 2023
Reviewers invited by journal
23 Jan, 2023
Editor assigned by journal
23 Jan, 2023
Submission checks completed at journal
23 Jan, 2023
First submitted to journal
22 Jan, 2023
You are reading this latest preprint version