  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.
