New Properties of Holomorphic Sobolev–Hardy Spaces

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