Search results for "Perron-type integral"

showing 2 items of 2 documents

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
researchProduct

THE HKr-INTEGRAL IS NOT CONTAINED IN THE Pr-INTEGRAL

2022

We compare a Perron-type integral with a Henstock-Kurzweiltype integral, both having been introduced to recover functions from their generalized derivatives defined in the metric Lr. We give an example of an HKr-integrable function which is not Pr-integrable, thereby showing that the first integral is strictly wider than the second one.

Settore MAT/05 - Analisi MatematicaHenstock-Kurzweil-type integralgeneralized absolute continuityDerivative in LrPerron-type integral
researchProduct