 that $$\lim_{\varepsilon\downarrow 0}\operatorname*{ess\,sup}_{u\in (v,v+\varepsilon)} \left\|\int_0^s\psi_r\left[|u-r|^{H-0}-|v-r|^{H-0}\right]\delta B_r^{\frac{H}{0}+\frac{0}{0}}\right\|_{\mathbb{D}^{0,0}} 