Geodesic
Certain properties of Cesàro derivatives of higher orders
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2013), pp. 3-10 
A. V. Dergachev. Certain properties of Cesàro derivatives of higher orders. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2013), pp. 3-10. http://geodesic.mathdoc.fr/item/VMUMM_2013_3_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Burkill J.C., “The Cesàro–Perron scale of integration”, Proc. London Math. Soc. (2), 39:7 (1935), 541–552 | DOI | MR

[2] Cross G.E., “The expression of trigonometrical series in Fourier Form”, Can. J. Math., 12:4 (1960), 694–698 | DOI | MR

[3] Sargent W.L.C., “On the Cesàro derivates of a function”, Proc. London Math. Soc. (2), 40:3–4 (1935), 235–254 | MR

[4] Skvortsov V.A., “Nekotorye svoistva CP-integrala”, Matem. sb., 60:3 (1963), 304–324

[5] Saks S., Teoriya integrala, IL, M., 1949

[6] Zigmund A., Trigonometricheskie ryady, V 2 t, Mir, M., 1965 | MR

[7] Hardy G.H., “Weierstrass's nondifferentiable function”, Trans. Amer. Math. Soc., 17:3 (1916), 301–325 | MR

[8] Sargent W.L.C., “A descriptive definition of Cesàro–Perron integrals”, Proc. London Math. Soc. (2), 47:3, 4 (1941), 212–247 | MR

[9] Verblunsky S., “On a descriptive definition of Cesàro–Perron integrals”, J. London Math. Soc., 7:3 (1971), 326–333 | DOI | MR