Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2013, Number 3, Pages 3–10 (Mi vmumm401)  
This article is cited in 3 scientific papers (total in 3 papers)

Mathematics

Certain properties of Cesàro derivatives of higher orders

A. V. Dergachev

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (266 kB) Citations (3) English version article
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Abstract: 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.
Key words: Cesàro derivatives, Cesàro–Perron integral, approximate derivatives, VBG functions, Denjoy relations.
Funding agency Grant number
Russian Foundation for Basic Research 11-01-00321
Ministry of Education and Science of the Russian Federation НШ-979.2012.1
Received: 02.11.2011
English version:
Moscow University Mathematics Bulletin, 2013, Volume 68, Issue 3, Pages 131–137
DOI: https://doi.org/10.3103/S0027132213030017
Bibliographic databases:
Document Type: Article
UDC: 517.518.152
Language: Russian
Citation: A. V. Dergachev, “Certain properties of Cesàro derivatives of higher orders”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2013, no. 3, 3–10; Moscow University Mathematics Bulletin, 68:3 (2013), 131–137
Citation in format AMSBIB
\Bibitem{Der13}
\by A.~V.~Dergachev
\paper Certain properties of Ces\`aro derivatives of higher orders
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2013
\issue 3
\pages 3--10
\mathnet{http://mi.mathnet.ru/vmumm401}
\transl
\jour Moscow University Mathematics Bulletin
\yr 2013
\vol 68
\issue 3
\pages 131--137
\crossref{https://doi.org/10.3103/S0027132213030017}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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