| Title: |
On the Lr-differentiability of two Lusin classes and a full descriptive characterization of the HKr-integral |
| Authors: |
Musial, Paul; Skvortsov, Valentin Anatol'evich; Sworowski, Piotr; Tulone, Francesco |
| Contributors: |
Musial, Paul; Skvortsov, Valentin Anatol'evich; Sworowski, Piotr; Tulone, Francesco |
| Publication Year: |
2025 |
| Collection: |
IRIS Università degli Studi di Palermo |
| Subject Terms: |
Lr-derivative; Lr-Henstock-Kurzweil integral; Denjoy integral; Lusin's class ACG; class ACGr; Settore MATH-03/A - Analisi matematica |
| Description: |
It is proved that any function of a Lusin-type class, the class of ACGr-functions, is differentiable almost everywhere in the sense of a derivative defined in the space Lr, 1 ≤ r < ∞. This leads to a full descriptive characterization of a Henstock-Kurzweil-type integral, the HKr-integral, which serves to recover functions from their Lr-derivatives. The class ACGr is compared with the classical Lusin class ACG and it is shown that continuous ACG-functions can fail to be Lr-differentiable almost everywhere. |
| Document Type: |
article in journal/newspaper |
| Language: |
English |
| Relation: |
info:eu-repo/semantics/altIdentifier/wos/WOS:001554261800002; volume:216; issue:6; firstpage:46; lastpage:58; numberofpages:13; journal:SBORNIK MATHEMATICS; https://hdl.handle.net/10447/682109 |
| DOI: |
10.4213/sm10129 |
| Availability: |
https://hdl.handle.net/10447/682109; https://doi.org/10.4213/sm10129 |
| Rights: |
info:eu-repo/semantics/closedAccess |
| Accession Number: |
edsbas.E866780E |
| Database: |
BASE |