On the Sharpness of the Estimate in a Theorem Concerning the Half Smoothness of a Function Holomorphic in a Ball

Let B n be the unit ball and S n be the unit sphere in C n , n ≥ 2. Let 0 < α < 1, and define a function f on as follows: The main result of the paper is the following theorem: the function ζ ↦ | f (ζ)| on the unit sphere S n belongs to the Hölder class H α ( S n ), while the function f does n...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2020-03, Vol.243 (6), p.985-992
Main Author: Shirokov, N. A.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Sharpness
Smoothness
Theorems
Citations: Items that this one cites
Online Access:Get full text
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Summary:Let B n be the unit ball and S n be the unit sphere in C n , n ≥ 2. Let 0 < α < 1, and define a function f on as follows: The main result of the paper is the following theorem: the function ζ ↦ | f (ζ)| on the unit sphere S n belongs to the Hölder class H α ( S n ), while the function f does not belong to the Hölder class for any ε > 0 .
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-019-04599-x