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Hardy spaces of the conjugate Beltrami equation |
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| Authors: | Laurent Baratchart Emmanuel Russ |
| Affiliation: | a INRIA Sophia Antipolis Méditerranée, 2004 route des Lucioles, BP 93, 06902 Sophia-Antipolis, France b Université de Provence, CMI, 39 rue F. Joliot-Curie, F-13453 Marseille Cedex 13, France c LATP, CNRS, UMR 6632, France d Université Paul Cézanne, Faculté des Sciences et Techniques de Saint-Jérôme, Avenue Escadrille Normandie-Niémen, 13397 Marseille Cedex 20, France |
| Abstract: | 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<p<∞. 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 div(σ∇u)=0 with Lp boundary data. |
| Keywords: | Hardy spaces Conjugate Beltrami equation Trace Non-tangential maximal function |
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