On the Hodge decomposition in R^n

TL;DR

This paper extends the Hodge decomposition to L^p differential forms in Euclidean space and Lizorkin currents, and computes the L_{qp}-cohomology of R^n, advancing understanding of geometric analysis.

Contribution

It provides a new L^p Hodge decomposition in Euclidean space and generalizes it to Lizorkin currents, along with calculating the L_{qp}-cohomology of R^n.

Findings

Established L^p Hodge decomposition for differential forms in R^n

Generalized decomposition to Lizorkin currents

Computed L_{qp}-cohomology of Euclidean space

Abstract

We prove a version of the $L^p$ hodge decomposition for differential forms in Euclidean space and a generalization to the class of Lizorkin currents. We also compute the $L_{qp}-$cohomology of $\mathbb{R}^n$.