0000000000089842

AUTHOR

Paul Musial

showing 2 related works from this author

The Lr-Variational Integral

2022

AbstractWe define the $$L^r$$ L r -variational integral and we prove that it is equivalent to the $$HK_r$$ H K r -integral defined in 2004 by P. Musial and Y. Sagher in the Studia Mathematica paper The$$L^{r}$$ L r -Henstock–Kurzweil integral. We prove also the continuity of $$L^r$$ L r -variation function.

Non-absolute integral.Settore MAT/05 - Analisi MatematicaGeneral MathematicsHKr IntegralLr-Variational Integral
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Comparison of the P-integral with Burkill's integrals and some applications to trigonometric series

2023

It is proved that the $P_r$-integral [9] which recovers a function from its derivative defined in the space $L^r$, 1 ≤r<∞, is properly included in Burkill’s trigonometric CP-and SCP-integrals. As an application to harmonic analysis, a de La Vallée-Poussin-type theorem for the $P_r$-integral is obtained: convergence nearly everywhere of a trigonometric series to a $P_r$-integrable function f implies that this series is the Pr-Fourier series of f.

Settore MAT/05 - Analisi MatematicaApplied MathematicsNon-absolute integral Derivative in $L^r$ Perron-type integral Cesaro-Perron integral Trigonometric series Fourier coefficients.AnalysisJournal of Mathematical Analysis and Applications
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