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

TL;DR

This paper introduces an extrapolation method for wavelet characterization of function spaces and extension operators, emphasizing smoothness properties without convexification, and refines existing extension results.

Contribution

It develops an extrapolation approach that avoids convexification for wavelet-based characterization of function spaces and improves a recent extension operator theorem.

Findings

Wavelet characterization of ball Banach function spaces

Extension of vector-valued inequalities

Refinement of Zhu, Yang, and Yuan's extension operator result

Abstract

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.