Hardy spaces of the conjugate Beltrami equation

Details Hardy spaces of the conjugate Beltrami equation Hardy spaces of the conjugate Beltrami equation

2009-07-04

arxiv.org/abs/0907.0744v2

Journal of Functional Analysis 259 (2010) 384-427

Mathematics

Complex Variables

Scientific paper

10.1016/j.jfa.2010.04.004

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 ${div}(\sigma\nabla u)=0$ with $L^p$-boundary data.

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