Applications of extrapolations to wavelet characterization of various function spaces and extension operators

The aim of this paper is to apply an extrapolation result without relying on convexification. We characterize ball Banach function spaces in terms of wavelets, formulated in a way that takes into account the smoothness properties of the spaces under consideration. The same technique can also be applied to prove vector-valued inequalities, for example. Furthermore, the result presented here refines a recent extension operator result by Zhu, Yang, and Yuan.