A study of Jacobians in Hardy-Orlicz spaces

We study the Jacobian determinants J = det(partial derivative f(i)/partial derivative x(j)) of mappings f: Omega subset of R-n --> R-n in a Sobolev-Or licz space W-1,W-Phi(Omega, R-n). Their natural generalizations are the wed ge products of differential forms. These products turn out to be in the Har dy-Orlicz spaces H-p(Omega). Other nonlinear quantities involving the Jacob ian, such as J log \J\, are also studied. In general, the Jacobians may cha nge sign and in this sense our results generalize the existing ones concern ing positive Jacobians.