On Lip(ω)-Continuity of the Operator of Harmonic Reflection Over Boundaries of Simple Carathéodory Domains

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On Lip(ω)-Continuity of the Operator of Harmonic Reflection Over Boundaries of Simple Carathéodory Domains. / Borovik, E. V.; Fedorovskiy, K. Yu.

In: Journal of Mathematical Sciences (United States), Vol. 251, No. 2, 01.11.2020, p. 200-206.

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

BibTeX

@article{084a3eee010148d1832f11ca6aa213ec,

title = "On Lip(ω)-Continuity of the Operator of Harmonic Reflection Over Boundaries of Simple Carath{\'e}odory Domains",

abstract = "We study continuity conditions for the operator of harmonic reflection of functions over boundaries of simple Carath{\'e}odory domains. This operator is considered as one acting from a space of functions of Lipschitz–H{\"o}lder 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).",

author = "Borovik, {E. V.} and Fedorovskiy, {K. Yu}",

note = "Publisher Copyright: {\textcopyright} 2020, Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2020",

month = nov,

day = "1",

doi = "10.1007/s10958-020-05079-3",

language = "English",

volume = "251",

pages = "200--206",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "2",

}

RIS

TY - JOUR

T1 - On Lip(ω)-Continuity of the Operator of Harmonic Reflection Over Boundaries of Simple Carathéodory Domains

AU - Borovik, E. V.

AU - Fedorovskiy, K. Yu

PY - 2020/11/1

Y1 - 2020/11/1

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=85093818207&partnerID=8YFLogxK

U2 - 10.1007/s10958-020-05079-3

DO - 10.1007/s10958-020-05079-3

M3 - Article

AN - SCOPUS:85093818207

VL - 251

SP - 200

EP - 206

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 2

ER -

ID: 86668663