On modulus of continuity of differentiation operator on weighted Sobolev   classes
  In this paper we investigate the modulus of continuity of differential operator of order $k$, $k\in\mathbb{N}$, on the classes of functions defined on half-line that have positive non-increasing continuous majorants of functions and their higher derivatives. 
Vladyslav Babenko, Oleh Kovalenko
math.FA