On
-reflection of harmonic functions and
-approximation by harmonic polynomials
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Published:2020-08-01
Issue:8
Volume:211
Page:1159-1170
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ISSN:1064-5616
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Container-title:Sbornik: Mathematics
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language:
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Short-container-title:Sb. Math.
Author:
Paramonov P. V.,Fedorovskiy K. Yu.
Abstract
Abstract
We obtain several new sharp
-continuity conditions, both necessary and sufficient, for operators of harmonic reflection of functions over boundaries of simple Carathéodory domains in
. These results are based on a new criterion (also obtained in this paper) for
-continuity of the Poisson operator in the aforesaid domains. As corollaries, we give new sufficient conditions for
-approximability of functions by harmonic polynomials on boundaries of simple Carathéodory domains in
.
Bibliography: 17 titles.
Funder
Russian Foundation for Basic Research
Simons Foundation
Ministry of Science and Higher Education of the Russian Federation
Subject
Algebra and Number Theory