Hardy spaces of the conjugate Beltrami equation Baratchart, Laurent; Leblond, Juliette; Rigat, St├ęphane; ...

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Baratchart, Laurent ; Leblond, Juliette ; Rigat, St├ęphane ; Russ, Emmanuel
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Journal of Functional Analysis
mathematics - complex variables; mathematics - analysis of pdes; [math:math_cv] mathematics/complex variables
To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.jfa.2010.04.004 Byline: Laurent Baratchart (a), Juliette Leblond (a), Stephane Rigat (b)(c), Emmanuel Russ (c)(d) Keywords: Hardy spaces; Conjugate Beltrami equation; Trace; Non-tangential maximal function 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<[infinity]. 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(Iau)=0 with L.sup.p boundary data. Author Affiliation: (a) INRIA Sophia Antipolis Mediterranee, 2004 route des Lucioles, BP 93, 06902 Sophia-Antipolis, France (b) Universite de Provence, CMI, 39 rue F. Joliot-Curie, F-13453 Marseille Cedex 13, France (c) LATP, CNRS, UMR 6632, France (d) Universite Paul Cezanne, Faculte des Sciences et Techniques de Saint-JerA[acute accent]me, Avenue Escadrille Normandie-Niemen, 13397 Marseille Cedex 20, France Article History: Received 27 July 2009; Accepted 6 April 2010 Article Note: (miscellaneous) Communicated by J. Coron
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