Generalized derivatives and integrals of Cesaro-Perron type. II / A. V. Dergachev. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2014. № 6. P. 3-10 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 0].

Several equivalent definitions of Ck-derivative and CkP-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 CkP-integral.

Key words: Cesaro derivatives, Cesaro-Perron integral, Marcinkiewicz property.