Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 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
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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.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00417
Ministry of Education and Science of the Russian Federation НШ-3682.2014.1
Received: 30.05.2012
English version:
Moscow University Mathematics Bulletin, 2014, Volume 69, Issue 6, Pages 229–236
DOI: https://doi.org/10.3103/S0027132214060011
Bibliographic databases:
Document Type: Article
UDC: 517.518.126
Language: Russian
Citation: A. V. Dergachev, “Generalized derivatives and integrals of Cesàro–Perron type. II”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2014, no. 6, 3–10; Moscow University Mathematics Bulletin, 69:6 (2014), 229–236
Citation in format AMSBIB
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\paper Generalized derivatives and integrals of Ces\`aro--Perron type.~II
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2014
\issue 6
\pages 3--10
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\transl
\jour Moscow University Mathematics Bulletin
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\vol 69
\issue 6
\pages 229--236
\crossref{https://doi.org/10.3103/S0027132214060011}
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