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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Limiting fractional and Lorentz space estimates of differential forms


Author: Jean Van Schaftingen
Journal: Proc. Amer. Math. Soc. 138 (2010), 235-240
MSC (2000): Primary 35B65; Secondary 26D10, 35F05, 42B20, 46E30, 46E35, 58A10
Published electronically: September 3, 2009
MathSciNet review: 2550188
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Abstract: We obtain estimates in Besov, Triebel-Lizorkin and Lorentz spaces of differential forms on $ \mathbf{R}^n$ in terms of their $ L^1$ norm.


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Additional Information

Jean Van Schaftingen
Affiliation: Département de Mathématique, Université Catholique de Louvain, Chemin du Cyclotron 2, 1348 Louvain-la-Neuve, Belgium
Email: Jean.VanSchaftingen@uclouvain.be

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10005-9
PII: S 0002-9939(09)10005-9
Keywords: Differential forms, div-curl system, Hodge decomposition, exterior differential, Besov spaces, Triebel--Lizorkin spaces, Lorentz-Sobolev spaces, regularity, limiting embedding
Received by editor(s): March 12, 2009
Received by editor(s) in revised form: April 20, 2009
Published electronically: September 3, 2009
Additional Notes: The author is supported by the Fonds de la Recherche Scientifique–FNRS
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.