Local 𝐋¹ estimates for elliptic systems of complex vector fields

Hounie, J.; Picon, T.

doi:10.1090/S0002-9939-2014-12219-2

Local $\mathbf {L}^{1}$ estimates for elliptic systems of complex vector fields
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by J. Hounie and T. Picon

Proc. Amer. Math. Soc. 143 (2015), 1501-1514

DOI: https://doi.org/10.1090/S0002-9939-2014-12219-2

Published electronically: December 9, 2014

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Abstract:

In this paper we present a strong local version of the Gagliardo-Nirenberg estimate that holds for elliptic systems of vector fields with smooth complex coefficients. We also consider $L^1$ estimates on forms analogous to those known in the case of the de Rham complex on $\mathbb {R}^N$.

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