B^{n+\alpha}_{p,q}(\mathbb R)=\left\{f\in W^{n,p}(\mathbb R) \Bigg| \int_0^\infty \left|\frac{\sup_{|h|<t}\|f^{(n)}(x+2h)-2f^{(n)}(x+h)+f^{(n)}(x)\|_p}{t^\alpha}\right|^q\frac{\mathrm dt}t<\infty \right\}