Weak-type operators and the strong fundamental lemma of real interpolation theory

@article{N2005,
abstract = {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 $L^\{p\}$ 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.},
author = {N. Krugljak, Y. Sagher, P. Shvartsman},
journal = {Studia Mathematica},
keywords = {interpolation theory; weak-type operators; strong fundamental lemma},
language = {eng},
number = {2},
pages = {173-201},
title = {Weak-type operators and the strong fundamental lemma of real interpolation theory},
url = {http://eudml.org/doc/284636},
volume = {170},
year = {2005},
}

TY - JOUR
AU - N. Krugljak
AU - Y. Sagher
AU - P. Shvartsman
TI - Weak-type operators and the strong fundamental lemma of real interpolation theory
JO - Studia Mathematica
PY - 2005
VL - 170
IS - 2
SP - 173
EP - 201
AB - 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 $L^{p}$ 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.
LA - eng
KW - interpolation theory; weak-type operators; strong fundamental lemma
UR - http://eudml.org/doc/284636
ER -