i need help with an result of a Riesz p-variation.
Please check the Riesz p-variation in the following link: https://www.researchgate.net/publication/328541764_On_bounded_second_Riesz_p-variablevariation/fulltext/5bd34d67299bf1124fa62a3e/On-bounded-second-Riesz-p-variablevariation.pdf
Definition 3 and 4 of the PDF explain the Riesz p-variation.
Theorem: Let $1 < p < \infty$, and $f:[0,1] \rightarrow \mathbb{R}$ such that $f \in RBV_p$ then $f \in AC$ where AC is the set of absolutely continous functions and $f' \in L_p$. Moreover, $$RVar_p(f) = \int_0^1 |f'(t)|^pdt$$
My attempt:
We know that $$Lip \subset\ RBV_p \subset AC \subset BV$$
Note: BV is the set of bounded variation function of Jordan.
As $f$ in $RBV_p$ then $f\in AC$, i.e f is absolutely continous function, this implies that $f$ is uniformly continous function.
Moreover, as $f\in RBV_p$ then $f\in BV$ and this implies that f is Riemann-Integrable then $f$ is differentiable.
In this step i'm stuck. Can someone help me?
