\begin{align} J:C[0,1]\rightarrow C[0,1], \quad f \rightarrow (J f)(x)=\int_0^1\frac{f(y)}{\lvert x-y\lvert^c} dy \end{align} For which $c>0$ is $(J f)_{f\in C[0,1]}$ equicontinous?
For $c\geq 1$ it's clear that $Jf$ is not even bounded. But for $c<1$ I don't even know how to prove that $Jf\in C[0,1]$. I'd like to use the dominated convergence theorem, but that will be difficult since $\frac{1}{\lvert x-y\lvert^c}$ is not bounded.