6533b7d6fe1ef96bd1265baa

RESEARCH PRODUCT

Comparison of the P-integral with Burkill's integrals and some applications to trigonometric series

Paul MusialValentin SkvortsovFrancesco Tulone

subject

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

description

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.

yearjournalcountryeditionlanguage
2023-07-01Journal of Mathematical Analysis and Applications
https://doi.org/10.1016/j.jmaa.2023.127019