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On \({{\,\mathrm{\textit{Lip}}\,}}^m\)-reflection of harmonic functions over boundaries of simple Carathéodory domains

Analysis and Mathematical Physics volume 9, pages 1031–1042 (2019)Cite this article

Abstract

We obtain several new sharp necessary and sufficient \({{\,\mathrm{\textit{Lip}}\,}}^m\)-continuity conditions for operators of harmonic reflection of functions over boundaries of simple Carathéodory domains in \({\mathbb {R}}^N\). These results are based on our \({{\,\mathrm{\textit{Lip}}\,}}^m\)-continuity criterion for the Poisson operator in the aforementioned domains.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    Petr Paramonov

  2. Bauman Moscow State Technical University, Moscow, Russia

    Konstantin Fedorovskiy & Petr Paramonov

  3. St. Petersburg State University, St. Petersburg, Russia

    Konstantin Fedorovskiy

Authors
  1. Konstantin Fedorovskiy
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  2. Petr Paramonov
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Correspondence to Konstantin Fedorovskiy.

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This work was supported by the Ministry of Science and Higher Education of the Russian Federation in the frameworks of the projects 1.3843.2017/4.6 (Konstantin Fedorovskiy and Petr Paramonov), and 1.517.2016/1.4 (Konstantin Fedorovskiy). Moreover, Konstantin Fedorovskiy was partially supported by the Simons foundation (Simons-IUM fellowship).

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Fedorovskiy, K., Paramonov, P. On \({{\,\mathrm{\textit{Lip}}\,}}^m\)-reflection of harmonic functions over boundaries of simple Carathéodory domains. Anal.Math.Phys. 9, 1031–1042 (2019). https://doi.org/10.1007/s13324-019-00296-9

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  • DOI: https://doi.org/10.1007/s13324-019-00296-9

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