English

An HK$_r$-integrable function which is P$_s$-integrable for no $s$

Classical Analysis and ODEs 2024-08-05 v2

Abstract

Given arbitrary r1r\ge1, we construct an HKr_r-integrable function which is not P1_1-integrable. This is an extension of Musial et al.\ construction published recently in [Musial, P., Skvortsov, V., Tulone, F.: The HKr_r-integral is not contained in the Pr_r-integral. Proc. Amer. Math. Soc. {\bf150}(5), 2107--2114 (2022)].

Cite

@article{arxiv.2403.11733,
  title  = {An HK$_r$-integrable function which is P$_s$-integrable for no $s$},
  author = {Piotr Sworowski},
  journal= {arXiv preprint arXiv:2403.11733},
  year   = {2024}
}
R2 v1 2026-06-28T15:24:08.194Z