$L^p$-theory for the tangential Cauchy-Riemann equation

Christine Laurent-Thiébaut (1)

1 IF - Institut Fourier

We are interested in $L^p$-theory for the tangential Cauchy-Riemann operator in locally embeddable, $s$-concave, generic CR manifolds. We study the Dolbeault isomorphism and develop the Andreotti-Grauert theory in that setting. Using Serre duality, we solve the tangential Cauchy-Riemann equation with exact support and $L^p$-estimates.

Mots clés: tangential Cauchy-Riemann equation; Serre duality; L^p estimates

Domaines: Variables complexes [math.CV]

Christine Laurent-Thiébaut. $L^p$-theory for the tangential Cauchy-Riemann equation. 2013. ⟨hal-00802093⟩