Generalized Kurzweil-Stieltjes integrals
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00643300" target="_blank" >RIV/67985840:_____/25:00643300 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.46753/pjaa.2025.v012i01.008" target="_blank" >https://doi.org/10.46753/pjaa.2025.v012i01.008</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.46753/pjaa.2025.v012i01.008" target="_blank" >10.46753/pjaa.2025.v012i01.008</a>
Alternative languages
Result language
angličtina
Original language name
Generalized Kurzweil-Stieltjes integrals
Original language description
Motivated by Malý and Kuncová (2019), we study a scale of generalized Kurzweil-Stieltjes integrals on the real line. Our first generalization is based on the concept of p-oscillation instead of ordinary oscillation, which was the key concept in their definition. Since Kurzweil-Stieltjes integral can be equivalently defined using ordinary oscillation, our improvement consists in using p-oscillation instead of ordinary one and α-systems instead of partitions of the interval. These changes lead to a larger classes of integrable functions. The key concepts like p-oscillation and p-median are discussed in detail. The integrals introduced are non-absolutely convergent and cover both the Lebesgue and Henstock-Kurzweil integral. Our main results concern e.g. the uniqueness of the indefinite generalized integrals and the dependence of the classes of integrable functions on the parameters p ∈ [1, ∞] and α ≥ 1. At the end, an analogue of the known Hake’s theorem is presented.
Czech name
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Czech description
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Classification
Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Poincare Journal of Analysis & Applications
ISSN
2349-6789
e-ISSN
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Volume of the periodical
12
Issue of the periodical within the volume
1
Country of publishing house
IN - INDIA
Number of pages
28
Pages from-to
113-140
UT code for WoS article
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EID of the result in the Scopus database
2-s2.0-105018480956