Comparison of the \(P_r\)-integral with Burkill's integrals and some applications to trigonometric series

DOI10.1016/J.JMAA.2023.127019OpenAlexW4315798429MaRDI QIDQ2697701

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

Publication date: 13 April 2023

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2023.127019

zbMATH Keywords

Fourier coefficientstrigonometric seriesnon-absolute integralPerron-type integralCesaro-Perron integralderivative in \(L^r\)

Mathematics Subject Classification ID

Real functions (26-XX) Functions of one variable (26Axx) Harmonic analysis in one variable (42Axx)

Cites Work

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• The \(L^r\)-variational integral
• On descriptive characterizations of an integral recovering a function from its \(L^r\)-derivative
• A note on trigonometric series
• Integrals and Trigonometric Series
• ON INTEGRATION BY PARTS IN BURKILL'S $ SCP$-INTEGRAL
• The L^rHenstock–Kurzweil integral
• Perron's integral for derivatives in $L^{r}$
• Integrals and Trigonometric Series
• The 𝐻𝐾ᵣ-integral is not contained in the 𝑃ᵣ-integral

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