6533b862fe1ef96bd12c625b
RESEARCH PRODUCT
On Descriptive Characterizations of an Integral Recovering a Function from Its $$L^r$$-Derivative
P. MusialV. A. SkvortsovF. Tulonesubject
generalized absolute continuity of a functionHenstock–Kurzweil-type integralabsolutely continuous measureSettore MAT/05 - Analisi MatematicaGeneral MathematicsLr-derivativeLr-variational measuredescription
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
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2022-04-01 |