Geodesic
Generalized derivatives and integrals of Ces\`aro--Perron type.~II
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2014), pp. 3-10

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Several equivalent definitions of $C_k$-derivative and $C_kP$-integral of Burkill are shown to behave better than the original definitions in certain cases. In particular, a Marcinkiewicz-type theorem is established for a modified definition of $C_kP$-integral. 
@article{VMUMM_2014_6_a0,
     author = {A. V. Dergachev},
     title = {Generalized derivatives and integrals of {Ces\`aro--Perron} {type.~II}},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {3--10},
     publisher = {mathdoc},
     number = {6},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2014_6_a0/}
}
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A. V. Dergachev. Generalized derivatives and integrals of Ces\`aro--Perron type.~II. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2014), pp. 3-10. http://geodesic.mathdoc.fr/item/VMUMM_2014_6_a0/