The characterisation of the regularity of the Jacobian determinant in the framework of potential spaces

Preprint series: 97-08, Analysis

The paper is published: J. London Math. Soc., 59 (1), 287-310, 1999

MSC:
46E35 Sobolev spaces and other spaces of smooth'' functions, embedding theorems, trace theorems

Abstract: We give necessary and sufficient conditions on the parameters $s_1, s_2, \ldots, s_m, p_1, p_2, \ldots, p_m$ such that the Jacobian determinant extends to a bounded operator from
$\dot{{\cal H}}^{s_1}_{p_1} \times \dot{{\cal H}}^{s_2}_{p_2} \times \ldots \times \dot{{\cal H}}^{s_m}_{p_m}$ into ${\cal Z}'$.
Here all spaces are defined on ${Bbb R}$ and $2 \le m \le n$.
In almost all cases the regularity of the Jacobian determinant is calculated exactly.

Keywords: potential spaces, Jacobian determinant, paraproducts