Matematičeskie zametki, Tome 17 (1975) no. 2, pp. 231-244
Citer cet article
P. Oswald. On the moduli of continuity of equimeasurable functions in the classes $\varphi(L)$. Matematičeskie zametki, Tome 17 (1975) no. 2, pp. 231-244. http://geodesic.mathdoc.fr/item/MZM_1975_17_2_a5/
@article{MZM_1975_17_2_a5,
author = {P. Oswald},
title = {On the moduli of continuity of equimeasurable functions in the classes $\varphi(L)$},
journal = {Matemati\v{c}eskie zametki},
pages = {231--244},
year = {1975},
volume = {17},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1975_17_2_a5/}
}
TY - JOUR
AU - P. Oswald
TI - On the moduli of continuity of equimeasurable functions in the classes $\varphi(L)$
JO - Matematičeskie zametki
PY - 1975
SP - 231
EP - 244
VL - 17
IS - 2
UR - http://geodesic.mathdoc.fr/item/MZM_1975_17_2_a5/
LA - ru
ID - MZM_1975_17_2_a5
ER -
%0 Journal Article
%A P. Oswald
%T On the moduli of continuity of equimeasurable functions in the classes $\varphi(L)$
%J Matematičeskie zametki
%D 1975
%P 231-244
%V 17
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_1975_17_2_a5/
%G ru
%F MZM_1975_17_2_a5
In the note we establish a number of relations between the moduli of continuity of the equimeasurable functions $f(x)$ and $f^*(x)$. In particular, for $f(x)\in L_p(0,1)$, $1\le p<\infty$, we have proved the inequality $\omega_p(\delta,f)\ge\frac12\omega_p(\delta,f^*),\quad\delta\in\Bigl[0,\frac12\Bigr]$.
