  We develop a new real-variable method for weighted $L^p$ estimates. The
method is applied to the study of weighted $W^{1, 2}$ estimates in Lipschitz
domains for weak solutions of second-order elliptic systems in divergence form
with bounded measurable coefficients. It produces a necessary and sufficient
condition, which depends on the weight function, for the weighted $W^{1,2}$
estimate to hold in a fixed Lipschitz domain with a given weight. Using this
condition, for elliptic systems in Lipschitz domains with rapidly oscillating,
periodic and VMO coefficients, we reduce the problem of weighted estimates to
the case of constant coefficients.
