  We study certain generalized Cauchy integral formulas for gradients of
solutions to second order divergence form elliptic systems, which appeared in
recent work by P. Auscher and A. Ros\'en. These are constructed through
functional calculus and are in general beyond the scope of singular integrals.
More precisely, we establish such Cauchy formulas for solutions $u$ with
gradient in weighted $L_2(\R^{1+n}_+,t^{\alpha}dtdx)$ also in the case
$|\alpha|<1$. In the end point cases $\alpha= \pm 1$, we show how to apply
Carleson duality results by T. Hyt\"onen and A. Ros\'en to establish such
Cauchy formulas.
