We prove that the classical Prandtl, Ishlinskii and Preisach hysteresis operators are continuous in Sobolev spaces $W^{1,p}(0,T)$ for $1\le p<+\infty$, (localy) Lipschitz continuous in $W^{1,1}(0,T)$ and discontinuous in $W^{1,\infty }(0,T)$ for arbitrary $T>0$. Examples show that this result is optimal.