Abstract and Applied Analysis
Volume 7 (2002), Issue 5, Pages 239-257

Commutators in real interpolation with quasi-power parameters

Ming Fan

Institute of Mathematics and Natural Sciences, Dalarna University College, Borlänge 781 88, Sweden

Received 20 December 2001

Copyright © 2002 Ming Fan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The basic higher order commutator theorem is formulated for the real interpolation methods associated with the quasi-power parameters, that is, the function spaces on which Hardy inequalities are valid. This theorem unifies and extends various results given by Cwikel, Jawerth, Milman, Rochberg, and others, and incorporates some results of Kalton to the context of commutator estimates for the real interpolation methods.