Matematičeskie zametki, Tome 12 (1972) no. 5, pp. 523-530
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A. P. Terekhin. Functions of bounded $p$-variation with given order of modulus of $p$-continuity. Matematičeskie zametki, Tome 12 (1972) no. 5, pp. 523-530. http://geodesic.mathdoc.fr/item/MZM_1972_12_5_a3/
@article{MZM_1972_12_5_a3,
author = {A. P. Terekhin},
title = {Functions of bounded $p$-variation with given order of modulus of $p$-continuity},
journal = {Matemati\v{c}eskie zametki},
pages = {523--530},
year = {1972},
volume = {12},
number = {5},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_5_a3/}
}
TY - JOUR
AU - A. P. Terekhin
TI - Functions of bounded $p$-variation with given order of modulus of $p$-continuity
JO - Matematičeskie zametki
PY - 1972
SP - 523
EP - 530
VL - 12
IS - 5
UR - http://geodesic.mathdoc.fr/item/MZM_1972_12_5_a3/
LA - ru
ID - MZM_1972_12_5_a3
ER -
%0 Journal Article
%A A. P. Terekhin
%T Functions of bounded $p$-variation with given order of modulus of $p$-continuity
%J Matematičeskie zametki
%D 1972
%P 523-530
%V 12
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_1972_12_5_a3/
%G ru
%F MZM_1972_12_5_a3
We construct continuous functions for which the modulus of $p$-continuity tends to zero with given order in Wiener's sense $$ V^p(\delta;f)=\sup\sum_i|f(x_i)-f(x_{i-1})|^p\qquad(p>1) $$ (the upper bound is taken over partitions satisfying the condition $x_i-x_{i-1}\leqslant\delta$).
