Global Smoothness Preservation by General Operators

Abstract

In this chapter we search the conditions under which global smoothness of a function f (as measured by its modulus of continuity) is preserved by the elements of general approximating sequences (L _n f). As one consequence we obtain statements concerning the invariance of Lipschitz classes under operators of several types. An important tool in our approach is the least concave majorant of a modulus of continuity. Here we follow the basic study done by the first author, Cottin and Gonska [22].