Abstract
AbstractGiven arbitrary $$r\ge 1$$
r
≥
1
, we construct an HK$$_r$$
r
-integrable function which is not P$$_1$$
1
-integrable. This is an extension of a recently published construction [Musial, P., Skvortsov, V., Tulone, F.: The HK$$_r$$
r
-integral is not contained in the P$$_r$$
r
-integral. Proceedings of the American Mathematical Society 150(5), 2107–2114 (2022)].
Publisher
Springer Science and Business Media LLC
Reference3 articles.
1. Gordon, L.: Perron’s integral for derivatives in $$L^{r}$$. Studia Math. 28, 295–316 (1967)
2. Musial, P., Sagher, Y.: The $$L^{r}$$ Henstock–Kurzweil integral. Studia Math. 160(1), 53–81 (2004)
3. Musial, P., Skvortsov, V., Tulone, F.: The HK$$_r$$-integral is not contained in the P$$_r$$-integral. Proc. Amer. Math. Soc. 150(5), 2107–2114 (2022)