Théorie $L^p$ pour l'équation de Cauchy-Riemann

Christine Laurent-Thiébaut (1)

1 IF - Institut Fourier

In this paper we propose a systematic study of the Cauchy-Riemann operator in the $L^p$-setting in complex manifolds. We first consider $L^p_{loc}$-theory and then we develop an $L^p$ Andreotti-Grauert theory. Finally we consider Serre duality and its applications to the solvability of the Cauchy-Riemann equation with exact support in $L^p$-spaces.

Mots clés: équation de Cauchy-Riemann; dualité de Serre; estimations $L^p$

Domaines: Variables complexes [math.CV]

Christine Laurent-Thiébaut. Théorie $L^p$ pour l'équation de Cauchy-Riemann. 2013. ⟨hal-00771193⟩