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JOURNALS // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika // Archive

Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2014 Number 6, Pages 3–10 (Mi vmumm357)

Mathematics

Generalized derivatives and integrals of Cesàro–Perron type. II

A. V. Dergachev

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: 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.

Key words: Cesàro derivatives, Cesàro–Perron integral, Marcinkiewicz property.

UDC: 517.518.126

Received: 30.05.2012


 English version:
Moscow University Mathematics Bulletin, Moscow University Måchanics Bulletin, 2014, 69:6, 229–236

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