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This article is cited in 3 scientific papers (total in 3 papers)
On Descriptive Characterizations of an Integral Recovering a Function from Its $L^r$-Derivative
P. Musiala, V. A. Skvortsovb, F. Tulonec a Chicago State University
b Moscow Center for Fundamental and Applied Mathematics
c Università degli Studi di Palermo
Abstract:
The notion of $L^r$-variational measure generated by a function $F\in L^r[a,b]$ is introduced and, in terms of absolute continuity of this measure, a descriptive characterization of the $H\!K_r$-integral recovering a function from its $L^r$-derivative is given. It is shown that the class of functions generating absolutely continuous $L^r$-variational measure coincides with the class of $ACG_{r}$-functions which was introduced earlier, and that both classes coincide with the class of the indefinite $H\!K_{r}$-integrals under the assumption of $L^r$-differentiability almost everywhere of the functions consisting these classes.
Keywords:
$L^r$-derivative, Henstock–Kurzweil-type integral, $L^r$-variational measure, absolutely continuous measure, generalized absolute continuity of a function.
Received: 07.09.2021
Citation:
P. Musial, V. A. Skvortsov, F. Tulone, “On Descriptive Characterizations of an Integral Recovering a Function from Its $L^r$-Derivative”, Mat. Zametki, 111:3 (2022), 411–421; Math. Notes, 111:3 (2022), 414–422
Linking options:
https://www.mathnet.ru/eng/mzm13284https://doi.org/10.4213/mzm13284 https://www.mathnet.ru/eng/mzm/v111/i3/p411
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Abstract page: | 158 | Full-text PDF : | 12 | References: | 29 | First page: | 8 |
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