Reading a paper, they use the fact that the function $x \mapsto \log |\det Df(x)|$ is $v$-Hölder, where $Df$ is the derivative of some map. Then, they state that the function $f$ is $C^{1+v}$ and continue the paper with this assumption. Does the condition of $f$ being $C^{1+v}$ imply the Hölder continuity of $\log|\det Df(x)|$?
Thanks