Dual space of Bessel potential space

Question

We define the Bessel potential space on $\mathbb{R}^n$ as $$H^{s,p}(\mathbb{R}^n)=\{u\in \mathcal{S}’(\mathbb{R}^n)| (I-\Delta )^{\frac s2}u\in L^p \} $$ where $(I-\Delta)^{\frac s2}u= \mathcal{F}^{-1} \left((1+|\xi|^2 )^\frac s2\hat u \right)$. It is known that $H^{s,p}(\mathbb{R}^n)=W^{s,p}(\mathbb{R}^n)$ when $s\in \mathbb{N}$. Moreover, we define $W^{-s,p}(\mathbb{R}^n)=(W^{s,p’}(\mathbb{R}^n ) )’$. So does this definition correspond to Bessel’s case? that is, does $H^{-s,p}=(H^{s,p’})’$?