Limiting fractional and Lorentz spaces estimates of differential forms

TL;DR

This paper derives estimates for differential forms in various advanced function spaces on R^n, linking their behavior to their L^1 norms, which enhances understanding of their regularity and integrability properties.

Contribution

It introduces new estimates in Besov, Lizorkin-Triebel, and Lorentz spaces for differential forms based on their L^1 norms, expanding the analytical tools available for such forms.

Findings

Estimates in Besov spaces for differential forms

Estimates in Lizorkin-Triebel spaces for differential forms

Estimates in Lorentz spaces for differential forms

Abstract

We obtain estimates in Besov, Lizorkin-Triebel and Lorentz spaces of differential forms on R^n in terms of their L^1 norm.