The \(L^r\)-variational integral

DOI10.1007/S00009-021-01962-8zbMath1503.26014OpenAlexW4220864998MaRDI QIDQ2120548

Paul M. Musial, Francesco Tulone

Publication date: 1 April 2022

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00009-021-01962-8

zbMATH Keywords

non-absolute integral\(HK_r\) integral\(L^r\)-variational integral

Mathematics Subject Classification ID

Denjoy and Perron integrals, other special integrals (26A39) Set functions and measures on spaces with additional structure (28C99)

Related Items (3)

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

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• Henstock type integral in compact zero-dimensional metric space and quasi-measures representations
• 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
• Generalized Hake property for integrals of Henstock type
• A version of Hake's theorem for Kurzweil-Henstock integral in terms of variational measure
• On the almost everywhere convergence of multiple Fourier-Haar series
• Generality of Henstock-Kurzweil type integral on a compact zero-dimensional metric space
• 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

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