Ultra‐differentiable classes and intersection theorems

Abstract

The aim of the paper is to study the relation between ultra‐differentiable classes of functions defined in terms of estimates on derivatives on one hand and in terms of growth properties of Fourier transforms of suitably localized functions in the class on the other hand. We establish this relation for the ultra‐differentiable classes introduced in , , and show that the classes of , , can be regarded as inhomogeneous Gevrey classes in the sense of . We also discuss a number of properties of the weight functions used to define the respective classes and of their Young conjugates.