New Properties of Holomorphic Sobolev-Hardy Spaces

We give new characterizations of the optimal data space for the $L^p(bD,\sigma )$-Neumann boundary value problem for the $\bar{\mathrm{\partial }}$ operator associated to a bounded, Lipschitz domain $D\subset \mathbb{C}$. We show that the solution space is embedded (as a Banach space) in the Dirichlet space and that for $p=2$, the solution space is a reproducing kernel Hilbert space.