On Descriptive Characterizations of an Integral Recovering a Function from Its $$L^r$$-Derivative
- Authors: Musial, P.; Skvortsov, V. A.; Tulone, F.
- Publication year: 2022
- Type: Articolo in rivista
- OA Link: http://hdl.handle.net/10447/550939
Abstract
The notion of Lr-variational measure generated by a function F ∈ Lr[a, b] is introduced and, in terms of absolute continuity of this measure, a descriptive characterization of the HKr -integral recovering a function from its Lr-derivative is given. It is shown that the class of functions generating absolutely continuous Lr-variational measure coincides with the class of ACGr -functions which was introduced earlier, and that both classes coincide with the class of the indefinite HKr-integrals under the assumption of Lr-differentiability almost everywhere of the functions consisting these classes