Certain properties of Ces\`aro derivatives of higher orders
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2013), pp. 3-10
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It is shown that a function with Cesàro $C_2$-derivative greater than $-\infty$ everywhere on a segment is not necessarily VBG. We also construct a function having a finite approximate derivative almost everywhere on a segment, but its $C_2$-derivative is equal to $+\infty$ almost everywhere.
@article{VMUMM_2013_3_a0,
author = {A. V. Dergachev},
title = {Certain properties of {Ces\`aro} derivatives of higher orders},
journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
pages = {3--10},
publisher = {mathdoc},
number = {3},
year = {2013},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMUMM_2013_3_a0/}
}
A. V. Dergachev. Certain properties of Ces\`aro derivatives of higher orders. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2013), pp. 3-10. http://geodesic.mathdoc.fr/item/VMUMM_2013_3_a0/