Holder Space

$\left\{f:\underset{x\ne y\in \Omega }{\sup }\frac{|f(x)-f(y)|}{\Vert x-y{\Vert }^{\alpha }}<\infty \right\}$, i.e. a Vector Space satisfying a Holder condition for a given $\alpha \in {\mathbb{R}}^{+}$.