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


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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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).

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