We know topological manifolds and we know Lipschitz manifolds. It seems that "Hölder manifolds" should be somewhere in between but not much seems published about them.
In the context of this question, a Hölder manifold is a topological manifold equipped with an atlas whose transition functions are locally Hölder continuous (that is, belong to the Hölder class $C^\alpha$ for some fixed $\alpha \in (0,1)$.
The definition above just mimics the definition of Lipschitz manifolds.
What is known about Hölder manifolds, and is there any particular reason less has been published about them than other classes of manifolds?