Classes of generalized functions with finite type regularities

TL;DR

This paper introduces and analyzes new spaces of generalized functions aligned with classical function spaces, aiming to characterize the regularity of embedded distributions with finite type regularities.

Contribution

It provides a novel framework connecting generalized functions with Hölder, Zygmund, and Sobolev spaces, enhancing the understanding of distribution regularity.

Findings

Characterization of distribution regularity within new generalized function spaces.

Establishment of algebraic structures corresponding to classical function spaces.

Framework applicable to analyzing distribution regularities in various contexts.

Abstract

We introduce and analyze spaces and algebras of generalized functions which correspond to H\" older, Zygmund, and Sobolev spaces of functions. The main scope of the paper is the characterization of the regularity of distributions that are embedded into the corresponding space or algebra of generalized functions with finite type regularities.