In Functional Analysis by J. Cerda, the theorem 7.28 says:
theorem 7.8. If $s-k>n/2$ then $H^{s}(\mathbb{R}^n)\subset C^{k}(\mathbb{R}^n)$ (functions $k$ times differentiable) with $H^{s}(\mathbb{R}^n):=\left\{u\in L^2: \mathcal{F}^{-1}(1+|\xi|^2)^{s/2}\mathcal{F}(u))\in L^2\right\}$
Let $H^{s,p}(\mathbb{R}^n):=\left\{u\in L^p: \mathcal{F}^{-1}(1+|\xi|^2)^{s/2}\mathcal{F}(u)\in L^p\right\}$ Sobolev space.
I know that if $s>n/p$ then $H^{s,p}(\mathbb{R}^n)\subset C(\mathbb{R}^n)$ [Taylor,Partial Differential equations III, prop. 6.3, p.26]
Is there a similar result in the context of $L^p$? e.g.
If $s-k>n/p$, the Sobolev space $H^{s,p}(\mathbb{R}^n)\subset C^k(\mathbb{R}^n)$?