On C-reflection of harmonic functions and C m-approximation by harmonic polynomials

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On C-reflection of harmonic functions and C m-approximation by harmonic polynomials. / Paramonov, P. V.; Fedorovskiy, K. Yu.

In: Sbornik Mathematics, Vol. 211, No. 8, 08.2020, p. 1159-1170.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{de0be706c5d241839f2777710e679413,

title = "On C-reflection of harmonic functions and C m-approximation by harmonic polynomials",

abstract = "We obtain several new sharp C-continuity conditions, both necessary and sufficient, for operators of harmonic reflection of functions over boundaries of simple Carath{\'e}odory domains in RN. These results are based on a new criterion (also obtained in this paper) for C-continuity of the Poisson operator in the aforesaid domains. As corollaries, we give new sufficient conditions for C-approximability of functions by harmonic polynomials on boundaries of simple Carath{\'e}odory domains in RN. Bibliography: 17 titles. ",

keywords = "Cm-approximation by harmonic polynomials, Harmonic reflection operator, Lipschitz-Holder spaces, Poisson operator, Simple Carath eodory domain",

author = "Paramonov, {P. V.} and Fedorovskiy, {K. Yu}",

note = "Publisher Copyright: {\textcopyright} 2020 Russian Academy of Sciences (DoM) and London Mathematical Society.",

year = "2020",

month = aug,

doi = "10.1070/SM9295",

language = "English",

volume = "211",

pages = "1159--1170",

journal = "Sbornik Mathematics",

issn = "1064-5616",

publisher = "Turpion Ltd.",

number = "8",

}

RIS

TY - JOUR

T1 - On C-reflection of harmonic functions and C m-approximation by harmonic polynomials

AU - Paramonov, P. V.

AU - Fedorovskiy, K. Yu

PY - 2020/8

Y1 - 2020/8

N2 - We obtain several new sharp C-continuity conditions, both necessary and sufficient, for operators of harmonic reflection of functions over boundaries of simple Carathéodory domains in RN. These results are based on a new criterion (also obtained in this paper) for C-continuity of the Poisson operator in the aforesaid domains. As corollaries, we give new sufficient conditions for C-approximability of functions by harmonic polynomials on boundaries of simple Carathéodory domains in RN. Bibliography: 17 titles.

AB - We obtain several new sharp C-continuity conditions, both necessary and sufficient, for operators of harmonic reflection of functions over boundaries of simple Carathéodory domains in RN. These results are based on a new criterion (also obtained in this paper) for C-continuity of the Poisson operator in the aforesaid domains. As corollaries, we give new sufficient conditions for C-approximability of functions by harmonic polynomials on boundaries of simple Carathéodory domains in RN. Bibliography: 17 titles.

KW - Cm-approximation by harmonic polynomials

KW - Harmonic reflection operator

KW - Lipschitz-Holder spaces

KW - Poisson operator

KW - Simple Carath eodory domain

UR - http://www.scopus.com/inward/record.url?scp=85095129663&partnerID=8YFLogxK

U2 - 10.1070/SM9295

DO - 10.1070/SM9295

M3 - Article

AN - SCOPUS:85095129663

VL - 211

SP - 1159

EP - 1170

JO - Sbornik Mathematics

JF - Sbornik Mathematics

SN - 1064-5616

IS - 8

ER -

ID: 86668568