Regularly varying rates of decrease for moduli of continuity and Fourier transforms of functions on \({\mathbb{R}}^ d\)
The author describes the correspondence between the rates of decrease for various moduli of continuity of a function on \({\mathbb{R}}^ d\) and for the tail-integral of the function's Fourier transform. The rates of decrease are described in terms of the class \(RV_{-\alpha}\) (regularly varying functions with exp -\(\alpha\)) defined as the class of all measurable functions \(s: [0,\infty]\to [0,\infty]\) such that \(\forall w>0,\lim_{t\to \infty}(s(wt)/s(t))=w^{-\alpha}.\)
scientific article; zbMATH DE number 4214662
scientific article