Hardy spaces of the conjugate Beltrami equation

Laurent Baratchart (1) , Juliette Leblond (1) , Stéphane Rigat (2) , Emmanuel Russ (2)

1 APICS - Analysis and Problems of Inverse type in Control and Signal processing
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités

We study Hardy spaces of solutions to the conjugate Beltrami equation with Lipschitz coefficient on Dini-smooth simply connected planar domains, in the range of exponents $1<\infty$. We analyse their boundary behaviour and certain density properties of their traces. We derive on the way an analog of the Fatou theorem for the Dirichlet and Neumann problems associated with the equation $\mbox{div}(\sigma\nabla u)=0$ with $L^p$-boundary data.

Domaines: Variables complexes [math.CV]; Equations aux dérivées partielles [math.AP]

Laurent Baratchart, Juliette Leblond, Stéphane Rigat, Emmanuel Russ. Hardy spaces of the conjugate Beltrami equation. Journal of Functional Analysis, 2010, 259, pp.384-427. ⟨10.1016/j.jfa.2010.04.004⟩. ⟨hal-00401712v2⟩