Author:
Boris I. Golubov Moscow Institute of Physics and Technology Russia, 115409 Moscow, Kashirskoe shosse 31 Russia, 115409 Moscow, Kashirskoe shosse 31

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Summary  

For the fractional dyadic derivative and integral, the following analogues of two theorems of Lebesgue  are proved: the theorem on differentiation of the indefinite Lebesgue integral of  an integrable function at its Lebesgue points, and the theorem on reconstruction of an absolutely  continuous function by means of its derivative. Dyadic fractional analogues of the formula of integration by  parts are also obtained. In addition, some theorems are proved on dyadic fractional differentiation and  integration of a Lebesgue integral depending on a parameter.  Most of the results are new even for dyadic derivatives and integrals of natural order.

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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)