This article is cited in 12 papers

On the Hodge decomposition in $\mathbb R^n$

Marc Troyanov

Section de Mathématiques, École Polytechnique Féderale de Lausanne, Lausanne, Switzerland

Abstract: We prove a version of $L^p$-Hodge decomposition for differential forms in Euclidean space and a generalization to the class of Lizorkin currents. Using these tools, we also compute $L_{q,p}$-cohomology of $\mathbb R^n$.

Key words and phrases: Hodge decomposition, temperate currents, Lizorkin currents.

MSC: 58A10, 42B, 42B20, 58A14

Received: January 11, 2008

Language: English

DOI: 10.17323/1609-4514-2009-9-4-899-926

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