A commutator theorem with applications

We give an extension of the commutator theorems of Jawerth, Rochberg and Weiss [9] for the real method of interpolation. The results are motivated by recentwork by Iwaniec and Sbordone [6] on generalized Hodge decompositions. The main estimates of these authors are based on a commutator theorem for a specific operator acting on $L^p$ spaces and through the use of the complex method of interpolation. In this note we give an extension of the Iwaniec-Sbordone theorem to general real interpolation scales.