Comptes Rendus
no. 9-10
Théorie spectrale, Théorie des opérateurs
On the necessity of the constant rank condition for L p estimates
André Guerra1 ; Bogdan Raiţă2
1 University of Oxford, Andrew Wiles Building, Woodstock Rd, Oxford OX2 6GG, United Kingdom
2 Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, 04103 Leipzig, Germany
Comptes Rendus. Mathématique, Volume 358 (2020) no. 9-10, pp. 1091-1095.

We consider a generalization of the elliptic L p -estimate suited for linear operators with non-trivial kernels. A classical result of Schulenberger and Wilcox (Ann. Mat. Pura Appl. 88 (1971), no. 1, p. 229-305) shows that if the operator has constant rank then the estimate holds. We prove necessity of the constant rank condition for such an estimate.

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Accepté le :
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DOI : 10.5802/crmath.105
Classification : 26D10, 42B20
André Guerra 1 ; Bogdan Raiţă 2

1 University of Oxford, Andrew Wiles Building, Woodstock Rd, Oxford OX2 6GG, United Kingdom
2 Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, 04103 Leipzig, Germany
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     journal = {Comptes Rendus. Math\'ematique},
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André Guerra; Bogdan Raiţă. On the necessity of the constant rank condition for $L^p$ estimates. Comptes Rendus. Mathématique, Volume 358 (2020) no. 9-10, pp. 1091-1095. doi : 10.5802/crmath.105. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.105/

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