Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 32, Tome 315 (2004), pp. 149-154
Citer cet article
N. A. Shirokov. Remark about the maximum of the modulus of an analytic function on the boundary. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 32, Tome 315 (2004), pp. 149-154. http://geodesic.mathdoc.fr/item/ZNSL_2004_315_a10/
@article{ZNSL_2004_315_a10,
author = {N. A. Shirokov},
title = {Remark about the maximum of the modulus of an analytic function on the boundary},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {149--154},
year = {2004},
volume = {315},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_315_a10/}
}
TY - JOUR
AU - N. A. Shirokov
TI - Remark about the maximum of the modulus of an analytic function on the boundary
JO - Zapiski Nauchnykh Seminarov POMI
PY - 2004
SP - 149
EP - 154
VL - 315
UR - http://geodesic.mathdoc.fr/item/ZNSL_2004_315_a10/
LA - ru
ID - ZNSL_2004_315_a10
ER -
%0 Journal Article
%A N. A. Shirokov
%T Remark about the maximum of the modulus of an analytic function on the boundary
%J Zapiski Nauchnykh Seminarov POMI
%D 2004
%P 149-154
%V 315
%U http://geodesic.mathdoc.fr/item/ZNSL_2004_315_a10/
%G ru
%F ZNSL_2004_315_a10
Let $\Lambda^{\alpha}$ be the analytic Hölder class in the unit disc $\mathbb D$. For $f\in \Lambda^{\alpha}$ and $I\subset\partial\mathbb D$, let $M_f(I)=\max_I|f|$. Assume that $I$, $J$ are arcs such that $|J|=2|I|$, $J$ and $I$ have common middle point. Then $$ M_f(J)\le C(\alpha,f)\frac{|I|^{\alpha}+M_f(I)}{\log^{\alpha}\Bigl(\frac{|I|^{\alpha}}{M_f(I)}+2\Bigr)}. $$ It is proved that this estimate cannot be improved.
