| Title: |
A new descriptive characterization of the HKr-integral and its inclusion in Burkill's integrals |
| Authors: |
Musial P.; Skvortsov V.; Sworowski P.; Tulone F. |
| Contributors: |
Musial P.; Skvortsov V.; Sworowski P.; Tulone F. |
| Publisher Information: |
Elsevier |
| Publication Year: |
2025 |
| Collection: |
IRIS Università degli Studi di Palermo |
| Subject Terms: |
Cesàro–Perron integral; Fourier coefficient; Henstock–Kurzweil-type integral; Lr-derivative; Non-absolute integral; Trigonometric series; Settore MATH-03/A - Analisi matematica |
| Description: |
We introduce a new class of functions, ACGr⁎, and compare it to the class of ACGr-functions which had been previously introduced by Musial and Sagher to characterize their Henstock–Kurzweil-type integral, the HKr-integral. We show that these two classes coincide and thereby we obtain a new descriptive characterization of the class of HKr-integrable functions. We then compare the HKr-integral with Burkill's CP-integral and obtain a de la Vallée Poussin-type theorem for the HKr-integral. |
| Document Type: |
article in journal/newspaper |
| Language: |
English |
| Relation: |
info:eu-repo/semantics/altIdentifier/wos/WOS:001301384800001; volume:542; issue:1; numberofpages:14; journal:JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS; https://hdl.handle.net/10447/665144 |
| DOI: |
10.1016/j.jmaa.2024.128758 |
| Availability: |
https://hdl.handle.net/10447/665144; https://doi.org/10.1016/j.jmaa.2024.128758 |
| Rights: |
info:eu-repo/semantics/closedAccess |
| Accession Number: |
edsbas.D05C476F |
| Database: |
BASE |