| Title: |
An Optimal Estimate of the $L^r$-$\delta$-Variation |
| Authors: |
Musial, Paul; Skvortsov, Valentin A.; Sworowski, Piotr; Tulone, Francesco |
| Contributors: |
Musial, Paul; Skvortsov, Valentin A.; Sworowski, Piotr; Tulone, Francesco |
| Publication Year: |
2025 |
| Collection: |
IRIS Università degli Studi di Palermo |
| Subject Terms: |
δ-variation; HKr-integral; partitioning property; Romanovski lemma; tagged partition; Settore MATH-03/A - Analisi matematica |
| Description: |
A notion of Lr-δ-variation of a function in Lr which plays an essential role in the theory of the Henstock-Kurzweil integral for functions in Lr (HKr-integral) is studied. We obtain an improved, in fact the best possible, estimate from below for this variation via the classical variation. We show that the class of functions having a finite Lr-δ-variation on an interval coincides with the class of functions of bounded variation on this interval. As a by-product of the results of the paper we obtain a new proof of the uniqueness of the HKr-integral. |
| Document Type: |
article in journal/newspaper |
| Language: |
English |
| Relation: |
info:eu-repo/semantics/altIdentifier/wos/WOS:001528089500012; numberofpages:11; journal:REAL ANALYSIS EXCHANGE; https://hdl.handle.net/10447/682107 |
| DOI: |
10.14321/realanalexch.1737532213 |
| Availability: |
https://hdl.handle.net/10447/682107; https://doi.org/10.14321/realanalexch.1737532213 |
| Rights: |
info:eu-repo/semantics/closedAccess |
| Accession Number: |
edsbas.FDE5509 |
| Database: |
BASE |