Analysis Mathematica
Volume/Issue:
Volume 38: Issue 1
О дифференциальных свойствах функций с ограниченной вариацией
Authors:
L. Bantsuri Department of Mathematics, Akaki Tsereteli State University, 59, Tamar Mepe St., Kutaisi, 4600 Georgia

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G. Oniani Department of Mathematics, Akaki Tsereteli State University, 59, Tamar Mepe St., Kutaisi, 4600 Georgia

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Pages:
1–17
Online Publication Date:
09 Feb 2012
Publication Date:
01 Mar 2012
Article Category:
Research Article
DOI:
https://doi.org/10.1007/s10476-012-0101-z
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Abstract  

It is established that Karagulyan’s exact estimate of the divergence rate of strong integral means of summable functions is extendable to strong means of additive functions of intervals having bounded variation. Furthermore, it is proved that each function defined on [0, 1]n with bounded variation in the sense of Hardy has a strong gradient at almost every point (this strengthens the corresponding result of Burkill and Haslam-Jones on the differentiability almost everywhere), whereas the same is not true for functions with bounded variation in the sense of Arzela.

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Cover Analysis Mathematica
Analysis Mathematica
Print ISSN:
0133-3852
Online ISSN:
1588-273X

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Analysis Mathematica
Language English
Size B5
Year of
Foundation		 1975
Volumes
per Year		 1
Issues
per Year		 4
Founder Akadémiai Kiadó
Founder's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0133-3852 (Print)
ISSN 1588-273X (Online)

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