Lipschitz and Dini–Lipschitz functions for the Sturm–Liouville transform

In this work, we introduce Lipschitz and Dini–Lipschitz classes of functions associated with the Sturm–Liouville operator L:=d2dx2+A′(x)A(x)ddx, where A is a nonnegative function satisfying certain conditions; and we prove two versions of Titchmarsh's theorems for the Sturm–Liouville transform F. The harmonic analysis associated with the operator L plays an important role in establishing the results of this paper.