ABSTRACT
In the first section we discuss some situations in which the strong-A00 condition arises. For instance, the Jacobian of a quasi conformal homeomorphism on R n is always strongly Aoo, by an argument of Gehring. We do not know if any reasonable converse to this statement holds. A necessary condition for a weight w to be the Jacobian of a q.c. mapping is that certain Sobolev and Poincare inequalities hold, to wit, the inequalities with respect tow that can be reduced to the standard case using the q.c. map as a change of variables. In Sections 2 and 3 we show that these inequalities always hold for a strongly Aoo weight.
