On the properties of functions of the Takagi power class

By construction, functions of Takagi power class are similar to Takagi's continuous nowhere differentiable function. These functions have one real parameter $p>0$. They are defined by the series $S_p(x) = \sum_{n=0}^\infty (T_0(2^nx)/2^n)^p$, where $T_0(x)$ is the distance from the real number $x$ to the nearest integer. We study such properties of functions $S_p(x)$ as continuity, generalized H\"older condition, global maxima and differentiability at the points $x=1/3$ and $x=2/3$, for various values of $p$.