We prove an interpolation theorem for weak-type operators. This is closely related to interpolation between weak-type classes. Weak-type classes at the ends of interpolation scales play a similar role to that played by BMO with respect to the interpolation scale. We also clarify the roles of some of the parameters appearing in the definition of the weak-type classes. The interpolation theorem follows from a K-functional inequality for the operators, involving the Calderón operator. The inequality was inspired by a K-J inequality approach developed by Jawerth and Milman. We show that the use of the Calderón operator is necessary. We use a new version of the strong fundamental lemma of interpolation theory that does not require the interpolation couple to be mutually closed.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm170-2-4,
author = {N. Krugljak and Y. Sagher and P. Shvartsman},
title = {Weak-type operators and the strong fundamental lemma of real interpolation theory},
journal = {Studia Mathematica},
volume = {166},
year = {2005},
pages = {173-201},
zbl = {1100.46014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm170-2-4}
}
N. Krugljak; Y. Sagher; P. Shvartsman. Weak-type operators and the strong fundamental lemma of real interpolation theory. Studia Mathematica, Tome 166 (2005) pp. 173-201. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm170-2-4/