We study continuity conditions for the operator of harmonic reflection of functions over boundaries of simple Carathéodory domains. This operator is considered as one acting from a space of functions of Lipschitz–Hölder type defined by a general modulus of a continuity, into another space of such kind. The results obtained are based on the continuity criterion for the Poisson operator (acting in the same spaces of functions) in the domains in question. This criterion is also obtained in the paper. These results generalize and refine those obtained in the recent work by the second author and P. Paramonov (Analysis and Mathematical Physics, 2019).

Original languageEnglish
Pages (from-to)200-206
Number of pages7
JournalJournal of Mathematical Sciences (United States)
Volume251
Issue number2
DOIs
StatePublished - 1 Nov 2020

    Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Applied Mathematics

ID: 86668663