Smoothness of a holomorphic function and its modulus on the boundary of a polydisk

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Smoothness of a holomorphic function and its modulus on the boundary of a polydisk. / Shirokov, N. A. .

In: Journal of Mathematical Sciences, Vol. 234, No. 3, 2018, p. 381-383.

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

BibTeX

@article{3b4618d05b654d9f918422054f5e0236,

title = "Smoothness of a holomorphic function and its modulus on the boundary of a polydisk",

abstract = "We prove that if a function f is holomorphic in the polydisk 픻 n, n ≥ 2, f is continuous in D n¯ , f(z) ≠ 0, z ∈ 픻 n, and |f| belongs to the α-H{\"o}lder class, 0 < α < 1, on the boundary of 픻 n, then f belongs to the (α2−ε)-H{\"o}lder class on D n¯ for any ε > 0. ",

author = "Shirokov, {N. A.}",

note = "Shirokov, N.A. Smoothness of a Holomorphic Function and Its Modulus on the Boundary of a Polydisk. J Math Sci 234, 381–383 (2018). https://doi.org/10.1007/s10958-018-4016-5",

year = "2018",

doi = "10.1007/s10958-018-4016-5",

language = "English",

volume = "234",

pages = "381--383",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "3",

}

RIS

TY - JOUR

T1 - Smoothness of a holomorphic function and its modulus on the boundary of a polydisk

AU - Shirokov, N. A.

N1 - Shirokov, N.A. Smoothness of a Holomorphic Function and Its Modulus on the Boundary of a Polydisk. J Math Sci 234, 381–383 (2018). https://doi.org/10.1007/s10958-018-4016-5

PY - 2018

Y1 - 2018

N2 - We prove that if a function f is holomorphic in the polydisk 픻 n, n ≥ 2, f is continuous in D n¯ , f(z) ≠ 0, z ∈ 픻 n, and |f| belongs to the α-Hölder class, 0 < α < 1, on the boundary of 픻 n, then f belongs to the (α2−ε)-Hölder class on D n¯ for any ε > 0.

AB - We prove that if a function f is holomorphic in the polydisk 픻 n, n ≥ 2, f is continuous in D n¯ , f(z) ≠ 0, z ∈ 픻 n, and |f| belongs to the α-Hölder class, 0 < α < 1, on the boundary of 픻 n, then f belongs to the (α2−ε)-Hölder class on D n¯ for any ε > 0.

UR - http://www.scopus.com/inward/record.url?scp=85052726741&partnerID=8YFLogxK

U2 - 10.1007/s10958-018-4016-5

DO - 10.1007/s10958-018-4016-5

M3 - Article

VL - 234

SP - 381

EP - 383

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 3

ER -

ID: 32482815