On descriptive characterizations of an integral recovering a function from its \(L^r\)-derivative

DOI10.1134/S0001434622030099zbMath1497.26007OpenAlexW4224509108MaRDI QIDQ2133821

Valentin A. Skvortsov, Francesco Tulone, Paul M. Musial

Publication date: 5 May 2022

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434622030099

zbMATH Keywords

absolutely continuous measure\(L^r\)-derivative\(L^r\)-variational measuregeneralized absolute continuity of functionHenstock-Kurzweil-type integral

Mathematics Subject Classification ID

Contents, measures, outer measures, capacities (28A12) Denjoy and Perron integrals, other special integrals (26A39)

Related Items (2)

On the relation between Denjoy-Khintchine and \(\operatorname{HK}_r \)-integrals ⋮ Comparison of the \(P_r\)-integral with Burkill's integrals and some applications to trigonometric series

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Multidimensional dyadic Kurzweil-Henstock- and Perron-type integrals in the theory of Haar and Walsh series
• Integration of functions ranging in complex Riesz space and some applications in harmonic analysis
• Variations and variational measures in integration theory and some applications
• Variational measure and sufficient differentiability condition of additive interval function
• A new full descriptive characterization of Denjoy-Perron integral
• On classes of functions generating absolutely continuous variational measures
• Real functions - current topics
• Generalized Hake property for integrals of Henstock type
• A version of Hake's theorem for Kurzweil-Henstock integral in terms of variational measure
• The \(L^r\)-variational integral
• On the almost everywhere convergence of multiple Fourier-Haar series
• Generality of Henstock-Kurzweil type integral on a compact zero-dimensional metric space
• Derivates of interval functions
• Kurzweil-Henstock type integral in fourier analysis on compact zero-dimensional group
• Kurzweil-Henstock type integral on zero-dimensional group and some of its applications
• Variational measures and the Kurzweil-Henstock integral
• On the Coefficients of Multiple Series with Respect to Vilenkin System
• The L^rHenstock–Kurzweil integral
• Perron's integral for derivatives in $L^{r}$
• A Hake-Type Theorem for Integrals with Respect to Abstract Derivation Bases in the Riesz Space Setting
• The 𝐻𝐾ᵣ-integral is not contained in the 𝑃ᵣ-integral

This page was built for publication: On descriptive characterizations of an integral recovering a function from its \(L^r\)-derivative