New Properties of Holomorphic Sobolev-Hardy Spaces

We give new characterizations of the optimal data space for the Lᵖ(bD,σ)-Neumann boundary value problem for the ∂̄ operator associated to a bounded, Lipschitz domain D. 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.