Besov regularity in non-linear generalized functions

TL;DR

This paper introduces new generalized function spaces related to Besov spaces, providing tools to analyze and detect Besov regularity of distributions with precise criteria.

Contribution

It develops novel modules and spaces of generalized functions linked to Besov spaces, expanding the analytical framework for distribution regularity detection.

Findings

Embedded classical Schwartz distribution spaces into new generalized spaces

Established criteria for detecting Besov regularity

Connected generalized functions with classical Besov space properties

Abstract

We introduce and study new modules and spaces of generalized functions that are related to the classical Besov spaces. Various Schwartz distribution spaces are naturally embedded into our new generalized function spaces. We obtain precise criteria for detecting Besov regularity of distributions.