  We develop a representation of the second kind for certain Hardy classes of
solutions to nonhomogeneous Cauchy-Riemann equations and use it to show that
boundary values in the sense of distributions of these functions can be
represented as the sum of an atomic decomposition and an error term. We use the
representation to show continuity of the Hilbert transform on this class of
distributions and use it to show that solutions to a Schwarz-type boundary
value problem can be constructed in the associated Hardy classes.
